02.

Decimal Fractions
3. Which is the smallest fraction among the
Type - 1 following fractions?
3 8 5 4
1. Which of the following fractions is the largest? , , ,
9 14 8 9
7 6 22 11
, , and 4 8
9 7 25 13 (a) (b)
11 22 9 14
(a) (b) 3 5
13 25 (c) (d)
7 6 9 8
(c) (d) RRB NTPC 02.03.2021 (Shift-I) Stage Ist
9 7
Ans. (c) :From question,
RRB NTPC (Stage-II) –16/06/2022 (Shift-II)
3 8
Ans. (b) : = 0.33 = 0.57
9 14
7
= 0.777 5 4
9 = 0.62 = 0.44
8 9
6 3
= 0.857 The smallest fraction is
7 9
22 3 3 11 5
= 0.88 4. Find the greatest fraction out of – , , , :
25 2 2 4 2
11 3 11
= 0.846 (a) (b)
13 2 4
5 3
22 (c) (d) –
Hence, fraction = 0.88 is the largest. 2 2
25 RRB NTPC 23.07.2021 (Shift-II) Stage Ist
2. Which of the following fractions is the Ans. (b) :
smallest?
3
9 11 – = –1.5
(a) (b) 2
11 12 3
8 10 = 1.5
(c) (d) 2
13 14 11
= 2.75
RRB NTPC 09.03.2021 (Shift-II) Stage Ist 4
Ans. (c) : From option, 5
= 2.5
9 2
= 0.8181 11
11 It is clear that greatest fraction is
4
11
= 0.916 5. Which of the following is the smallest fraction?
12
7 7 4 5
8 , , ,
= 0.615 6 9 5 7
13
7 4
10 (a) (b)
= 0.714 6 5
14
7 5
8 (c) (d)
Hence, it is clear that smallest fraction is . 9 7
13 RRB NTPC 22.02.2021 (Shift-I) Stage Ist
Decimal Fractions 51 YCT
 7 7 4 5 10. Find the greatest among these fractions.
Ans. (d) : = 1.16, = 0.77, = 0.80, = 0.71 5/11, 3/15, 12/11, 4/7, 9/12
6 9 5 7 (a) 12/11 (b) 3/15
5 (c) 9/12 (d) 4/7
Hence the smallest fraction is
7 RRB RPF-SI -10/01/2019 (Shift-I)
6. Which of the following fractions is the smallest? Ans : (a)
5 3 12 4 9
7 7 = 0.45, = 0.2, = 1.09, = 0.57, = 0.75
(a) (b) 11 15 11 7 12
8 10
12
3 5 Hence, the required largest fraction will be =
(c) (d) 11
4 7 11. Find the least among these fractions.
RRB NTPC 23.02.2021 (Shift-I) Stage Ist 1 1 9 500
Ans. (b) : On writing given fraction in descending , , ,
10 100 1000 10000
order.
500 1
7 3 5 7 (a) (b)
> > > 10000 100
8 4 7 10 1 9
0.875 > 0.75 > 0.714 > 0.70 (c) (d)
10 1000
7 RRB RPF Constable -17/01/2019 (Shift-I)
Hence, will be the smallest fraction.
10 Ans. (d) : From question,
7. Find the greatest among these fractions. 1
5/6, 6/11, 2/3, 8/9, 6/7 = 0.1
10
(a) 2/3 (b) 8/9 (c) 5/6 (d) 6/7 1
RRB JE - 01/06/2019 (Shift-III) = 0.01
Ans. (b) From question :- 100
9
5
= 0.83 ,
6
= 0.54 = 0.009
6 11 1000
500
2 8 = 0.05
= 0.67 , = 0.89 10000
3 9 0.1 > 0.05 > 0.01 > 0.009
6
= 0.85 Hence, it is clear that the required fraction is
9
.
7 1000
8
Hence, the greatest fraction is 0.89 = 12. Which of the following fractions is the
9 greatest?
8. Find the difference between the greatest and (a) 8/19 (b) 9/22
the least fraction among 2/3, 3/4, 4/5, 5/6. (c) 10/23 (d) 11/24
(a) 3/5 (b) 1/7 (c) 1/6 (d) 2/5 RRB RPF-SI -11/01/2019 (Shift-III)
RRB JE - 22/05/2019 (Shift-I)
Ans : (d) From options
Ans : (c) From question,
8 9 10 11
2 = 0.421, = 0.409, = 0.43, = 0.458
= 0.66 (Least fraction) 19 22 23 24
3 11
3 Hence, the required greatest fraction is .
= 0.75 24
4 13. Arrange the following ratios in decreasing
4 order, which number will be the last?
= 0.8 11:14, 17:21, 5:7, 2:3
5
(a) 17:21 (b) 5:7
5
= 0.83 (Greatest fraction) (c) 2:3 (d) 11:14
6 RRB Group-D – 05/10/2018 (Shift-II)
5 2 5−4 1 Ans. (c) The given proportional numbers are-
Hence, the required difference = − = =
6 3 6 6 11 17 5 2 33 34 30 28
, , , = , , ,
9. Which of the following is the greatest? 14 21 7 3 42 42 42 42
(a) 15/16 (b) 24/25 The decreasing order of the numbers,
(c) 34/35 (d) 19/20 17 11 5 2
RRB JE - 02/06/2019 (Shift-II) > > >
21 14 7 3
Ans. (c) 15/16 = 0.937 Hence, the last proportional number will be 2/3.
24/25 = 0.96
34/35 = 0.97 (the greatest fraction) 14. Which of the following fractions is the largest?
19/20 = 0.95 1 2 3 4
, , ,
Hence, option (c) is the greatest fraction. 8 12 16 20
Decimal Fractions 52 YCT
 3 4 Ans : (b) From option,
(a) (b) 29
16 20 = 0.376
1 2 77
(c) (d)
8 12 8
RRB Group-D – 12/10/2018 (Shift-III) = 0.380
21
1 5 25
Ans : (b) = 0.125 = 0.357 , = 0.378
8 14 66
2 8
= 0.166 Hence, it is clear that is the largest fraction.
12 21
3 18. Which of the following is the smallest fraction?
= 0.187
16 6 13 15 19 5
4 , , , ,
= 0.200 11 18 22 36 6
20 19 13
4
(a) (b)
Hence, it is clear that is the greatest fraction. 36 18
20 6 5
15. Which of the following fractions is the largest? (c) (d)
11 6
3 5 8 25 RRB Group-D – 24/10/2018 (Shift-II)
, , ,
15 20 64 1000 6 13 15 19 5
5 8 Ans. (a) : , , , ,
(a) (b) 11 18 22 36 6
20 64 6 13
3 25 = 0.54 , = 0.72
(c) (d) 11 18
15 1000 15 19
RRB Group-D – 10/10/2018 (Shift-III) 22 = 0.68 , 36
= 0.52
Ans : (a) From options– 5
5 8 = 0.83
(a) = 0.25 (b) = 0.125 6
20 64 19
3 25 Hence, it is clear that the smallest fraction is .
36
(c) = 0.2 (d) = 0.025
15 1000 8 6 5 9
5 19. , , ,
Hence, the largest fraction is . 6 4 3 5
20 The largest fraction among the given fractions
16. Which of the following is the smallest fraction? is:
4 5 3 6 5 6
, , , (a) (b)
9 4 8 7 3 4
3 4 9 8
(a) (b) (c) (d)
8 9 5 6
6 5 RRB Paramedical Exam – 20/07/2018 (Shift-III)
(c) (d)
7 4 8 6
Ans. (c) : = 1.33 , = 1.50
RRB Group-D – 16/10/2018 (Shift-II) 6 4
Ans : (a) From question, 5 9
4 5 = 1.66 , = 1.80
= 0.444 ⇒ = 1.25 3 5
9 4 9
Hence, it is clear that the required largest fraction is .
3 5
= 0.375 20. Which of the following is the smallest fraction?
8
6 3 5 8 25
= 0.857 , , ,
7 15 20 64 1000
3 8 25
Hence, it is clear that is the smallest fraction. (a) (b)
8 64 1000
17. Which of the following fractions is the largest? 5 3
(c) (d)
29 8 20 15
(a) (b) RRB Group-D – 15/10/2018 (Shift-II)
77 21
Ans : (b) From question,
5 25
(c) (d) 3 5
14 66 = 0.2, = 0.25
RRB Group-D – 16/10/2018 (Shift-II) 15 20

Decimal Fractions 53 YCT

 8 25 1 3
= 0.125, = 0.025 = 0.200 ⇒ = 0.428
64 1000 5 7
25 The descending order = 0.666>0.428>0.200>0.166
Hence, the required smallest fraction is .
1000 2 3 1 1
21. Which of the following fractions is the least of > > >
3 7 5 6
all?
(a) 6/5 (b) 4/3 2 3 1 1
(c) 3/2 (d) 5/4 ⇒ , , ,
3 7 5 6
RRB NTPC 29.03.2016 Shift : 3
Ans : (a) From option, 25. Arrange the following fractions in the
6 4 ascending order.
= 1.2, = 1.33
5 3 2 4 5 9
, , and
3 5 3 8 9 11
= 1.5, = 1.25
2 4 4 5 2 9 5 2 4 9
6 (a) < < < (b) < < <
Hence, it is clear that is the required least fraction of 8 9 3 11 9 3 8 11
5
all. 5 2 9 4 4 5 9 2
(c) < < < (d) < < <
22. The smallest of the fractions among 5/8, 3/4, 9 3 11 8 8 9 11 3
13/16, 7/12 is________. RRB NTPC 09.03.2021 (Shift-II) Stage Ist
(a) 5/8 (b) 3/4
(c) 13/16 (d) 7/12 Ans. (a) : From question,
RRB NTPC 27.04.2016 Shift : 2
Ans : (d) From question,
5 3 13
= 0.625, = 0.75, = 0.8125
8 4 16 (Ascending order),
7
= 0.58
12
7
Hence, the smallest fraction is .
12
23. Which of the following is a reducible fraction? 26. The fractions 1 , 4 , 2 written in ascending
91 79 3 7 5
(a) (b) order are:
15 26
105 41 1 4 2
(c) (d) (a) , , (b) All fractions are equal
112 17 3 7 5
RRB ALP & Tec. (09-08-18 Shift-II)
1 2 4 4 1 2
Ans : (c) A fraction whose fractional shares have a (c) , , (d) , ,
common factor, is called reducible fraction. 3 5 7 7 3 5
105 7 × 15 RRB NTPC 07.01.2021 (Shift-II) Stage Ist
=
112 7 ×16 1
Ans. (c) : = 0.33
3
Type - 2
4
= 0.57
24. The descending order of the fractions 7
2 1 1 3 2
, , , is: = 0.4
3 6 5 7 5
3 2 1 1 2 3 1 1 1 2 4
(a) , , , (b) , , , Hence ascending order = , ,
7 3 6 5 3 7 5 6 3 5 7
3 1 1 2 1 1 3 2 27. Select the option that given decimal numbers
(c) , , , (d) , , ,
7 6 5 3 6 5 7 3 0.25, 1.24, 0.0882 and 2.67 are arranged in
RRB NTPC 15.03.2021 (Shift-II) Stage I ascending order.
(a) 2.67, 1.24, 0.25, 0.0882
2
Ans. (b) : = 0.666 (b) 0.25, 1.24, 0.08821, 2.67
3 (c) 1.24, 0.25, 2.67, 0.0882
1 (d) 0.0882, 0.25, 1.24, 2.67
= 0.166
6 RRB NTPC 01.04.2021 (Shift-I) Stage Ist

Decimal Fractions 54 YCT

Ans. (d) : On arranging the given decimal numbers in 31. Arrange the given fractions in decreasing order
ascending order- 7 8 9
, ,
0.0882 → 0.25 → 1.24 → 2.67 8 9 10
Hence, option (d) is correct. 9 7 8 7 8 9
(a) , , (b) , ,
28. Which of the following fractions are in 10 10 9 8 9 10
ascending order? 9 8 7 8 7 9
(c) , , (d) , ,
12 14 16 14 12 16 10 9 8 9 8 10
(a) , , (b) , , RRB NTPC 15.02.2021 (Shift-I) Stage Ist
18 17 19 17 18 19
Ans. (c) : In the given fractions if the difference
16 14 12 12 16 14
(c) , , (d) , , between the numerator and denominator of certain
19 17 18 18 19 17 fractions are same then the fraction having greater
RRB NTPC 05.03.2021 (Shift-II) Stage Ist denominator will be greater fraction while the one
Ans. (a) : From options, having smaller denominator will be smaller fraction.
12 14 16 Hence the descending order of the fraction will be
= 0.66, = 0.82, = 0.84 9 8 7
18 17 19 , ,
12 14 16 10 9 8
Required ascending order = , , 32. Write the ratio 5 : 3, 7 : 5 and 6 : 4 in
18 17 19
descending order.
2 1
29. The ascending order of the fractions , and 5 7 6 7 6 5
3 2 (a) > > (b) > >
1 3 5 4 5 4 3
is-
6 5 6 7 6 7 5
2 1 1 2 1 1 (c) > > (d) > >
(a) , , (b) , , 3 4 5 4 5 3
3 2 6 3 6 2 RRB NTPC 18.01.2021 (Shift-I) Stage Ist
1 1 2 1 2 1
(c) , , (d) , , 5
6 2 3 6 3 2 Ans. (c) : = 1.67
RRB NTPC 26.07.2021 (Shift-I) Stage Ist 3
2 1 1 7
Ans. (c) : On equating the denominator , and of = 1.4
3 2 6 5
fractions we have, 6
2 4 = 1.5
= (Multiply by 2 numerator and denominator) 4
3 6
5 6 7
1 3
= (Multiply by 3 numerator and denominator) Hence descending order = > >
2 6 3 4 5
1 1 33. Select the option that gives the fractions
= 2 1 3 1 7 5
6 6 , , , , , in ascending order :
1 1 2 5 3 5 4 10 8
Hence ascending order of fractions = < <
6 2 3 1 1 2 3 5 7 7 5 3 2 1 1
30. In which of the following options are the (a) , , , , , (b) , , , , ,
4 3 5 5 8 10 10 8 5 5 3 4
fractions arranged in ascending order?
1 1 3 2 5 7 1 1 2 3 5 7
9 6 5 2 3 6 5 9 2 3 (c) , , , , , (d) , , , , ,
(a) , , , , (b) , , , , 4 3 5 5 8 10 3 4 5 5 8 10
11 7 6 5 8 7 6 11 5 8
RRB NTPC 10.01.2021 (Shift-I) Stage Ist
2 6 9 3 5 3 2 9 5 6
(c) , , , , (d) , , , , Ans. (a) : From question
5 7 11 8 6 8 5 11 6 7
2 1 3 1
RRB NTPC 27.03.2021 (Shift-II) Stage Ist = 0.4 , = 0.33 , = 0.6 , = 0.25 ,
Ans. (d) : From option (d), 5 3 5 4
7 5
3
= 0.375
2
= 0.40 = 0.7 , = 0.625
8 5 10 8
,
Hence, ascending order of given fractions
9 5
= 0.8181 = 0.8333 1 1 2 3 5 7
11 , 6 = , , , , ,
4 3 5 5 8 10
6
= 0.857 4 -7 5 -2
7 34. If the rational numbers , , , are
-9 18 -6 3
3 2 9 5 6 arranged in ascending order, then which of
Ascending order · < < < <
8 5 11 6 7 these numbers will be placed first?
Decimal Fractions 55 YCT
 4 −7 38. Which of the following is true for given
(a) (b) numbers?
−9 18
(a) 13/33<32/47<20/47<25/27
5 −2
(c) (d) (b) 13/33<20/47<25/27<32/27
−6 3
(c) 13/33<20/47<32/47<25/27
RRB Group-D – 02/11/2018 (Shift-II)
(d) 20/47<13/33<32/47<25/27
Ans. (c)
RRB RPF-SI -13/01/2019 (Shift-I)
4 −7 5 −2 Ans : (c) The given fractions–
Rational numbers = , , and
−9 18 −6 3 13 20
4 = 0.39, = 0.42
= – 0.44 33 47
−9 32 25
= 0.68, = 0.92
−7 47 27
= – 0.38
18 0.39 < 0.42 < 0.68 < 0.92
5 13 20 32 25
= – 0.83 Hence, < < < is true.
−6 33 47 47 27
−2 39. Which of the following is in descending order?
= – 0.66 (a) 2/3, 3/4, 4/5, 1/2 (b) 3/4, 4/5, 1/2, 2/3
3
The first number when placed in ascending order (c) 4/5, 3/4, 2/3, 1/2 (d) 4/5, 1/2, 2/3, 3/4
RRB RPF Constable -25/01/2019 (Shift-I)
5
= – 0.83 = Ans : (c) From option (c),
−6 4 3 2 1
35. Arrange the following fractions in descending 5 , 4 , 3 , 2
order. Q LCM of the denominators = 60
5/6, 3/7, 8/9, 3/14 Hence, again from option (c),
(a) 8/9, 5/6, 3/7, 3/14 (b) 8/9, 3/14, 3/7, 5/6 48 45 40 30
(c) 5/6, 8/9, 3/7, 3/14 (d) 3/7, 8/9, 5/6, 3/14 = > > >
RRB JE - 22/05/2019 (Shift-III) 60 60 60 60
4 3 2 1
Ans : (a) Hence, , , , are in descending order.
5 4 3 2
5 3 8 3
= 0.83, = 0.42, = 0.88, = 0.21 40. Whose ascending order from the following
6 7 9 14 numbers is correct?
Hence, the descending order of the fractions is 5 3 7 3 5 7
8 5 3 3 (a) , , (b) , ,
, , , . 6 5 9 5 6 9
9 6 7 14 3 7 5 7 3 5
36. Which of the following fractions are in (c) , , (d) , ,
5 9 6 9 5 6
descending order? RRB RPF Constable -20/01/2019 (Shift-I)
(a) 5/8, 7/12, 3/4, 13/16 Ans : (c) From options,
(b) 7/12, 13/16, 3/4, 5/8 The given fractions–
(c) 5/8, 7/12, 13/16, 3/4 5 3
(d) 13/16, 3/4, 5/8, 7/12 = 0.83 , = 0.6
6 5
RRB JE - 26/06/2019 (Shift-III)
7
Ans : (d) Arranging in descending order- = 0.77
(a) 5/8 = 0.62, 7/12 = 0.58, 3/4 = 0.75, 13/16 = 0.81 9
The required ascending order is 0.6, 0.77, 0.83
(b) 7/12 = 0.58, 13/16 = 0.81, 3/4 = 0.75, 5/8 = 0.62
3 7 5
(c) 5/8 = 0.62, 7/12 = 0.58, 13/16 = 0.81, 3/4 = 0.75 = , ,
(d) 13/16 = 0.81, 3/4 = 0.75, 5/8 = 0.62, 7/12 = 0.58 5 9 6
Hence, option (d) is in descending order. 41. Which among the following is the correct
37. Which of the following fractions are in ascending order of the numbers?
ascending order? 1 4 1 4
(a) , , 0.33 (b) , 0.33,
(a) 0.65, 0.76, 0.67, 0.86, 3 15 3 15
(b) 0.65, 0.86, 0.67, 0.76 4 1 4 1
(c) , 0.33, (d) 0.33, ,
(c) 0.65, 0.67, 0.76, 0.86 15 3 15 3
(d) 0.67, 0.65, 0.76, 0.86 RRB NTPC 17.01.2017 Shift-1
RRB RPF Constable -17/01/2019 (Shift-III) Ans : (c) From the given fractions,
Ans : (c) From option (c), 1 4
= 0.333, = 0.266 and 0.33
0.65 < 0.67 < 0.76 < 0.86 3 15
Hence, option (c) is in ascending order. 0.266<0.33<0.333
Decimal Fractions 56 YCT
 4 1 Ans. (a) : If the denominator of the given rational
< 0.33 < number is 5 then the rational number will represent the
15 3
terminating decimal.
Hence, the required ascending order of the numbers will
4 1 1 6
be ,0.33, . From option (a) 1 = = 1.2 (Terminating decimal)
15 3 5 5
42. Which of the following is correct for the given 1 37
numbers? (b) 4 = = 4.1 (Non-Terminating decimal)
(a) 13/21 < 57/97 < 52/94 < 36/79 9 9
(b) 36/79 < 57/97 < 52/94 < 13/21 1 22
(c) 36/79 < 52/94 < 13/21 < 57/97 (c) 3 = = 3.142857 (Non-Terminating decimal)
(d) 36/79 < 52/94 < 57/97 < 13/21 7 7
RRB NTPC 02.04.2016 Shift : 1 1 7
(d) 2 = = 2.3 (Non-Terminating decimal)
Ans : (d) From options– 3 3
13 57 46. Which of the following numbers has a
= 0.619, = 0.587
21 97 terminating decimal?
52 36 15 29 7 77
= 0.553, = 0.455 , , ,
94 79 600 343 22 × 7 2 210
36 52 57 13 7 29
Hence, < < < is correct order. (a) 2 2 (b)
79 94 97 21 2 ×7 343
43. Whose ascending order is correct from the 15 77
given fractions? (c) (d)
600 210
5 19 11 11 5 19 RRB NTPC 07.01.2021 (Shift-II) Stage Ist
(a) , , (b) , ,
8 24 16 16 8 24 Ans. (c) : In according to options, converting the
5 11 19 19 11 5 fractions into decimals
(c) , , (d) , ,
8 16 24 24 16 8 7 7
(a) 2 2 = = 0.0357.....
RRB NTPC 11.04.2016 Shift : 3 2 ×7 196
5 19 11 29
Ans : (c) = 0.625 = 0.791 = 0.687 (b) = 0.0845.....
8 24 16 343
Hence, the required ascending order is 0.625 < 0.687 < 15
(c) = 0.025
0.791 600
5 11 19 77
⇒ < < (d) = 0.36
8 16 24 210
15
Hence, from above is terminating decimal.
600
Type - 3 109
47. Decimal expansion of is:
31 100
44. The decimal expansion of will terminate 0 9 9
2.5 (a) 1 + + (b) 10 +
after: 10 100 100
(a) two decimal places 9 0
(c) 1 + (d) 100 + 9 +
(b) three decimal places 100 100
(c) more than three decimal places RRB NTPC 07.01.2021 (Shift-II) Stage Ist
(d) one decimal place
109 100 0 9
RRB NTPC 19.01.2021 (Shift-II) Stage Ist Ans. (a) : Decimal expansion of = + +
31 31×10 × 4 1240 100 100 10 100
Ans. (d) : = == 12.4 0 9
2.5 2.5 ×10 × 4 100 = 1+ +
10 100
i,e. the decimal expansion ends after one decimal place
Hence, option (a) is required answer.
45. Which of the following has terminating decimal
representation? 48. Which of the following rational numbers have
a non-terminating decimal expansion?
1 1
(a) 1 (b) 4 (a) 3 2
23
(b)
11
5 9 25 1000
1 1 42 19
(c) 3 (d) 2 (c) (d) 3 7 5
7 3 3252 257
RRB NTPC 19.01.2021 (Shift-II) Stage Ist RRB NTPC 07.04.2021 (Shift-II) Stage Ist
Decimal Fractions 57 YCT
Ans. (d) : From the given option- 52. Which of the following will have a terminating
23 23 decimal expansion?
(a) = = 0 ⋅ 115 57 47
2352 200 (a) (b)
120 150
11
(b) = 0⋅011 61 43
1000 (c) (d)
110 140
42 16 RRB Group-D – 20/09/2018 (Shift-II)
(c) 2 2 = = 0 ⋅ 071111....
35 225 Ans : (a) From options,
19 19 57
(d) 3 7 5 = (a) = 0.475
257 8 × 78125 × 16807 120
47
19 (b) = 0.313
= 150
10504375000
61
= 0.00000000181...... (c) = 0.5545
Hence it is clear from the given options that the decimal 110
43
expansion of option (d) is non – terminating. (d) = 0.30714285
140
8 57
49. Convert into a decimal number. Hence, will have a terminating decimal expansion.
9 120
(a) 0.85 (b) 0.88 53. Which of the following numbers will have a
(c) 0.91 (d) 0.77 value of terminating decimal?
RRB NTPC 05.03.2021 (Shift-II) Stage Ist 9 6
(a) (b)
8 45 45
Ans. (b) : Required decimal number = = 0.88 3 12
9 (c) (d)
3 45 45
50. The decimal expression of comes to an end RRB Group-D – 24/09/2018 (Shift-II)
8
9
after how many digits after the decimal? Ans : (a) = 0.2
(a) 2 (b) 4 45
(c) 3 (d) 5 6
RRB NTPC 20.01.2021 (Shift-I) Stage Ist = 0.1333
45
3 3
Ans. (c) : = 0.375 = 0.06667
8 45
The decimal range of 3/8 ends after the three digits of 12
decimal. = 0.26667
45
51. Which of the following is terminating decimal?
9
1 1 Hence, it is clear that the value of option (a) , is a
(a) (b) 45
32 24 terminating decimal.
1 1 54. Which of the following will give terminating
(c) (d)
96 48 decimal?
RRB RPF-SI -05/01/2019 (Shift-III) 12 6
Ans : (a) From options, (a) (b)
72 72
1
= 0.03125 (c)
9
(d)
3
32 72 72
1 RRB Group-D – 03/10/2018 (Shift-III)
= 0.416666667
24 12 1
1 Ans : (c) = = 0.166666 − − −
= 0.0104166667 72 6
96
6 1
1 = = 0.083333 − − −
= 0.0208333333 72 12
48
9 1
A terminating decimal is usually defined as a decimal = = 0.125
number that contains a finite number of digits after the 72 8
decimal point. 3 1
= = 0.041666 − − − −
1 72 24
∴ option (a) = 0.03125
32 9 1
Hence, it is terminating decimal. Hence, option (c) = = 0.125 is correct.
72 8

Decimal Fractions 58 YCT

55. Which of the following fractions will not have a 58. Which of the following fractions will be a
value in recurring decimal? terminating decimal?
6 12
20 25 (a) (b)
(a) (b) 144 144
56 56
3 9
10 21 (c) (d)
(c) (d) 144 144
56 56 RRB Group-D – 03/12/2018 (Shift-II)
RRB Group-D – 20/09/2018 (Shift-I) 6 3 1
Ans : (d) = = = 0.0416
Ans. (d) : From options 144 72 24
12 1
20 25 = = 0.083
(a) = 0.357142 (b) = 0.44642 144 12
56 56 3 1
= = 0.02083
10 21 144 48
(c) = 0.178571 (d) = 0.375
56 56 9 1
= = 0.0625
21 144 16
Hence, the value of option (d) = 0.375 is not in 9
56 Hence, it is clear that option (d) is a terminating
144
recurring decimal. decimal fraction.
56. Which of the following options is an example of 59. Which of the following will give a recurring
recurring decimal? decimal?
24 24 21 21
(a) (b) (a) (b)
60 90 30 120
24 24 21 21
(c) (d) (c) (d)
120 30 60 90
RRB ALP & Tec. (20-08-18 Shift-II)
RRB Group-D – 17/09/2018 (Shift-II)
21 21 21
Ans : (b) (a)
24
= 0.4 (b)
24
= 0.266 Ans : (d) = 0.7, = 0.175, = 0.35
60 90 30 120 60
24 24 21
(c) = 0.2 (d) = 0.8 = 0.23333 ⇒ 0.23
120 30 90
24 Hence option (d) will give recurring decimal.
Hence, option (b) is an example of recurring 60. Which of the following will give a terminating
90
decimal. decimal?
57. Which of the following vulgar fractions, when 3 12
(a) (b)
written as a decimal, its value will not be found 36 36
in a terminating decimal? 9 6
(c) (d)
27 21 36 36
(a) (b) RRB ALP & Tec. (10-08-18 Shift-III)
480 640
81 240 Ans : (c) From option (c),
(c) (d) 9 1
450 450 = = 0.25
RRB Group-D – 22/10/2018 (Shift-III) 36 4
Hence, it is clear that option (c) is a fraction of
27 terminating decimal.
Ans : (d) (a) = 0.05625
480 61. Which of the following fractions will not give a
21 recurring decimal:
(b) = 0.0328125
640 8 6
(a) (b)
81 56 56
(c) = 0.18
450 4 7
(c) (d)
240 56 56
(d) = 0.5333 = 0.53
450 RRB ALP & Tec. (09-08-18 Shift-III)
240 Ans : (d) From options,
Hence, it is clear that option (d) = 0.5333 = 0.53
450 8 6
(a) = 0.142857...... (b) = 0.107142......
is not giving a value in terminating decimal. 56 56
Decimal Fractions 59 YCT
 4 7 420
(c) = 0.071428...... (d) = 0.125 ⇒
56 56 990
Hence it is clear that option (d) will not give a recurring 14
decimal. =
33

Type - 4 x
65. If 0.372 = where x and y are co-prime, then
y
62. The value of 0.16 + 0.15 - 0.13 is the value of (x + y) ?
23 17 (a) 143 (b) 186
(a) (b) (c) 151 (d) 134
63 90
34 19 RRB Group-D 26/08/2022 (Shift-I)
(c) (d)
45 99 x 372 − 3
RRB GROUP-D – 17/08/2022 (Shift-III) Ans. (c) : = 0.372 =
y 990
Ans. (b) : 0.16 + 0.15 - 0.13
x 369
16 − 1 15 − 1 13 − 1 =
= + − y 990
90 90 90
x 41
15 14 12 =
= + − y 110
90 90 90
15 + 14 − 12 x + y = 41+110
=
90 = 151
17 66. 2.666 … + 2.77 … in fraction form is:
=
90 47 29
(a) (b)
63. The value of 9.467 – 2.467 + 4.467 9 9
10321 10321 31 49
(a) (b) (c) (d)
1100 900 9 9
10521 10521 RRB Group-D 18/08/2022 (Shift-I)
(c) (d) Asn. (d) : 2.666 ...... + 2.77.....
900 1100
RRB GROUP-D – 15/09/2022 (Shift-I) = 2.6 + 2.7
Ans. (b) : x = 9.46 7 – 2.46 7 + 4.46 7 6 7
= 2+ +2+
x = 11.46 7 9 9
x = 11.46777 ....(i) 6+7
=4 +
100x = 1146.777 ....(ii) 9
1000x = 11467.77 ....(iii) 13
meceer. (iii) – meceer. (ii) =4+
9
900x = 10321
36 + 13 49
10321 = =
x= 9 9
900
67. Simplify 1. 24 is an improper fraction.
p
64. Express 0.424 in the form , where p and q 123 124
q (a) (b)
are integers and q ≠ 0. 90 99
41 13 91 41
(a) (b) (c) (d)
165 33 90 33
14 41 RRB Group-D 22/08/2022 (Shift-I)
(c) (d) 24
33 990 Ans. (d) : 1.24 = 1 +
RRB GROUP-D – 17/08/2022 (Shift-II) 99
Ans. (c) : Given, 8
= 1+
⇒ 0.424 space where p and q are int egers and q ≠ 0 33
424 − 4 41
⇒ integers and q + o =
990 33

Decimal Fractions 60 YCT

 p p
68. Express 0.13241 in the form , where p and q 71. Express 4.567 in the form of where p and
q q
are integers and q ≠ 0. q are integeas and q ≠ 0
3287 3827 281 63
(a) (b) (a) 4 (b) 4
21780 24975 495 110
3337 3307 94 283
(c) (d) (c) 4 (d) 4
24160 24975 165 495
RRB Group-D 26/08/2022 (Shift-III) RRB Group-D 06/09/2022 (Shift-I)
Ans. (d) : Let x = 0.13241241 ------- (i) Ans. (a) : 4.567
On multiplying by 100 both side in above equation 567 − 5
100x = 13.241241 --------- (ii) = 4+
990
On multiplying by 100000 both side in the equation (i)
562
100000x = 13241.241241 ------- (ii) = 4+
990
On Subtracting eq (i) from eq (ii) –
281
99900x = 13228 = 4+
495
13228
x= 281
99900 =4
3307 495
x=
24975 p
72. Express 0.27 in the form where p and q are
Hence, option (d) is correct. q
69. If the mixed recurring decimal 0.23 45 is integers and q ≠ 0.
expressed as a fraction in its lowest term, then 18 18
(a) (b)
how much its denominator will more than 7 5
numertor ? 5 7
(a) 421 (b) 512 (c) (d)
18 18
(c) 627 (d) 375 RRB Group-D 24/08/2022 (Shift-I)
RRB Group-D 06/09/2022 (Shift-II)
p
Ans. (a) : Fractional form of recurring decimal 0.23 45 Ans. (c) : 0.27 = x(Let) =
q
p 2345 − 23
= x = 0.2777……………..(i)
q 9900 100x = 27.77…………..(ii)
p 2322 On subtracting equation (i) from equation (ii)
=
q 9900 275 5
99x = 27.5 ⇒ x = =
p 129 990 18
=
q 550 p 5
Hence, =
Required difference = 550 – 129 q 18
= 421 p
Hence its denominator will be 421 more than numerator. 73. Express 0.12 in the form , where p and q are
q
70. The correct expression of 8.46 in the fractional integers and q ≠ 0.
form is 6 4
(a) (b)
84 846 33 33
(a) (b)
99 99 5 7
83 838 (c) (d)
(c) (d) 33 33
99 99 RRB GROUP-D – 27/09/2022 (Shift-II)
RRB Group-D 13/09/2022 (Shift-III)
Ans. (b) : 0.12
Ans. (d) : 8.46
p 12 4
46 838 = =
=8+ = q 99 33
99 99
Decimal Fractions 61 YCT
74. The value of 0.56 + 0.43 + 0.89 is 5 103 101
= 1++ – –1
(a) 1.98 (b) 1.87 11 330 900
5 103 101
(c) 1.89 (d) 1.88 = + –
RRB NTPC 23.02.2021 (Shift-I) Stage Ist 11 330 900
4500 + 3090 − 1111
Ans. (c) : 0.56 + 0.43 + 0.89 =
9900
56 43 89
= + + 6479
99 99 99 =
9900
188 89
= = 1+ = 1.89 589
99 99 =
900
p
75. The number 0.12464 in the form is equal
q 78. Express the decimal number 3.127 in fraction
to: form
117 17 281 563
(a) (b) (a) (b)
1950 950 900 180
67 617 180 365
(c) (d) (c) (d)
4999 4950 563 180
RRB NTPC 14.03.2021 (Shift-I) Stage I RRB NTPC 22.02.2021 (Shift-I) Stage Ist
Ans. (d) : 0.12464 Ans. (b) : 3.127
12464 − 124 127 – 12 115
= · 3+ = 3+
99000 900 900
12340 617 23 563
= = 3+ =
99000 4950 180 180
76. The value of 3.14 is: 79. 0.532 ______ is equivalent to the fraction:
13 12 572 527
(a) 3 (b) 3 (a) (b)
90 90 990 990
11 14 537 32
(c) 3 (d) 3 (c) (d)
90 90 990 99
RRB NTPC 29.01.2021 (Shift-II) Stage I
RRB NTPC 04.02.2021 (Shift-II) Stage Ist
Ans. (a) : The value of 3.14
Ans. (b) : Let x = 0.532 _____(i)
14 − 1
= 3+ Multiplying by 10 in equation (i),
90 10x = 5.323232 …. ___(ii)
13 Again, multiplying by 100 in equation (i),
= 3+
90 1000 x = 532.3232 …. (iii)
13 Substracting equation (ii) from equation (iii),
=3 990 x = 527
90
527
77. Simplify 1.45 + 0.312 - 1.112 . x=
13 374 990
(a) (b)
20 495 80. 1.236576576 ... can be written in the form of:
589 163 125334 123534
(c) (d) (a) (b)
900 300 99000 99000
RRB NTPC 08.04.2021 (Shift-II) Stage Ist 123534 125434
(c) (d)
Ans. (c) : From question, 99900 99900
1.45 + 0.312 –1.112 RRB NTPC 12.01.2021 (Shift-II) Stage Ist
45 312 – 3  112 – 11  Ans. (c) : 1.236576576 ...........
= 1+ +0+ – 1 +
99 990  900  = 1 + 0.236576
5 309  101  236576 − 236
= 1+ + – 1+ =1+
11 990  900  999000

Decimal Fractions 62 YCT

 1235340 84.0.047619 , when written as a vulgar fraction, is
= equal to-
999000
1 1
123534 (a) (b)
= 21 19
99900 1 1
p (c) (d)
81. Express 0.037 in the form of , where p is a 23 17
q RRB Group-D – 19/09/2018 (Shift-II)
whole number and q is a natural number. Ans. (a) : From given number,
17 37 047619 1
(a) (b) 0.047619 = =
450 1000 999999 21
34 17 85. Convert 0.6 into fraction:
(c) (d) 6 2
99 45 (a) (b)
3 3
RRB NTPC 09.01.2021 (Shift-I) Stage Ist
2 4
Ans. (a) : Let, (c) (d)
6 3
x = 0.037 ...(i) RRB Group-D – 28/09/2018 (Shift-II)
Multiplying by 100 in equation (i), Ans. (b) : Given,
6 2
100x = 3.777 ...(ii) 0.6 = = , (From decimal fraction system)
9 3
Multiplying by 10 in equation (ii), 86. Which of the following fractions’ result will not
1000x = 37.777 ...(iii) be a recurring decimal?
n n
Subtracting eq (ii) from eq (iii) – 10 12
(a) (b)
900x = 34 30 30
14 8
34 17 (c) (d)
x= = 30 30
900 450 RRB Paramedical Exam – 21/07/2018 (Shift-III)
or Ans : (b) From options,
p 17 10 1
= (a) = = 0. 3
q 450 30 3
12 4 2
82. Evaluate: (b) = = = 0.4
30 10 5
0.623
14 7
623 23 (c) = = 0.4 6
(a) (b) 6 30 15
999 999 8 4
(d) = = 0.2 6
617 23 30 15
(c) (d) 6 Hence, it is clear that option (b) is not in recurring
990 990
decimal.
RRB JE - 31/05/2019 (Shift-II)
87. Which of the following vulgar fractions will not
Ans : (c) 0.623 end when represented in decimal?
623 − 6 81 80
= (From decimal fraction system) (a) (b)
990 150 150
617 15 21
= (c) (d)
990 48 600
RRB Group-D – 10/10/2018 (Shift-II)
83. What is the correct expression of 0.0654 [( ) Ans : (b) From options,
sign represents continuous decimal)]? 81
(a) = 0.54
18 18 150
(a) (b) 80
275 277 (b) = 0.5333333
654 150
(c) 654 (d) 15
1000 ( c ) = 0.3125
RRB RPF-SI -10/01/2019 (Shift-III) 48
21
Ans : (a) 0.0654 (d ) = 0.035
654 − 6 648 18 600
= = = Hence, it is clear that option (b) will not end when
9900 9900 275 represented in decimal.

Decimal Fractions 63 YCT

88. When 0.0236 when written as the simplest 1
Ans. (c) : Given,
form, what will be the obtained vulgar 450
fraction? On dividing,
13 13 0.0022
(a) (b)
1100 9999 450 1000
13 13 900
(c) (d)
3300 550 1000
RRB Group-D – 25/09/2018 (Shift-I)
900
Ans : (d) 0.0236
100
0.236
0.0236 = 1
10 Hence, = 0.002
236 − 2 234 450
= = 92. Express 0.0987 as a vulgar fraction in its lowest
10 × 990 9900
117 13 form?
= = 163 329
4950 550 (a) (b)
7 1650 9990
89. Express in the form of decimal. 326 163
11 (c) (d)
(a) 0.623 (b) 0.633 3300 1665
RRB Group-D – 08/10/2018 (Shift-III)
(c) 0.63 (d) 0.62
RRB Group-D – 25/09/2018 (Shift-II) Ans : (c) Let x = 0.0987
7 100x = 9.87 Multiplying by 100 in both side,
Ans : (c) The decimal of = 9.8787 ......
11 = 9.78 + 0.098787 .....
0.6363
100x = 9.78 + x
11 70
99x = 9.78
66 9.78
40 x=
99
33 978 326
= =
70 9900 3300
66 93. Which of the following fractions will give a
40 recurring decimal?
33 27 27
(a) (b)
7
60 72
Hence, in 0.6363, two digits of the number (6 and 3) are 27 27
(c) (d)
repeating itself. 48 84
RRB Group-D – 05/10/2018 (Shift-III)
90. Show 0.0836 in the form of vulgar fraction.
Ans. (d) From options
46 23 27 27
(a) (b) (a) = 0.45 (b) = 0.375
555 1100 60 72
23 828 27 27
(c) (d) (c) = 0.5625 (d) = 0.32142857
275 9900 48 84
RRB Group-D – 15/11/2018 (Shift-III) 27
Hence, the fraction , gives a recurring decimal.
Ans : (c) : 0.0836 = ? 84

836 – 8 94. If 0.41 is expressed as the vulgar fraction

= 41
9900 . Find n.
999.....9 ( n times )
828 23
= = (a) 1 (b) 3
9900 275 (c) 4 (d) 2
1 RRB Group-D – 01/10/2018 (Shift-III)
91. When , written as recurring decimal, it will
450 Ans : (d) Let 0.41 = x
be equal to: 0.414141 ..... = x
(a) 0.2 (b) 0.02 Multiplying by 100 in both sides,
(c) 0.002 (d) 0.0002 100x = 41.4141 .......
RRB Group-D – 12/10/2018 (Shift-I) 100x = 41 + x
Decimal Fractions 64 YCT
99x = 41 Ans. (a) : From question,
41 5 2 6
x= + −
99 100 5 25
Hence, it is clear that the number of digit 9 in 1 2 6
denominator is twice. So n = 2. = + −
20 5 25
95. Correct expression of 1.4 27 = ? (Bar sign 5 + 40 − 24
indicates to recurring decimal) =
100
1427 157
(a) (b) 21
1000 110 = = 0.21
1427 157 100
(c) (d)
10000 111
RRB NTPC 17.01.2017 Shift-3 Type - 5
Ans : (b) 1.427 = 1 + 427 1 1 1 1
427 − 4 99. The sum of + + + .... + is:
= 1+ 2 6 12 n(n + 1)
990
n +1 n(n + 1)
423 47 157 (a) (b)
= 1+ = 1+ = n 2
990 110 110
n +1 n
96. Correct expression of 0.0234 = ? (c) (d)
2n n +1
13 34 RRB NTPC 02.03.2021 (Shift-II) Stage Ist
(a) (b) 2
555 100 1 1 1 1
134 234 Ans. (d) : + + + .......+
(c) (d) 2 6 12 n ( n + 1)
990 1000
RRB NTPC 07.04.2016 Shift : 2 1 1 1 1
= + + + ...... +
Ans : (a) Rule for converting mixed-recurring decimal 1× 2 2 × 3 3 × 4 n ( n + 1)
fraction into common or vulgar fraction:- 1 1 1 1 1 1 1 1
firstly non-recurring part is subtracted from recurring = − + − + − + ...... + −
1 2 2 3 3 4 n ( n + 1)
part, as numerator, then take 9, equal to the number of
recurring digits, and add 0, equal to the number of non- 1 1
= −
recurring digits, as denominator. 1 ( n + 1)
From question,
n +1 −1 n
234 − 0 = =
0.0234 = n +1 n +1
9990
234 78 13 100. Express 32 : 20 in its lowest form.
= = = (a) 8 : 5 (b) 8 :10
9990 3330 555 (c) 16 : 10 (d) 24 : 15
44 4 0.4 RRB NTPC 31.01.2021 (Shift-I) Stage Ist
97. Express %+ %+ % in the form of
5 5 5 32 20
decimal number. Ans. (a) : 32 : 20 = : =8:5
4 4
(a) 0.0888 (b) 0.0998
(c) 0.0896 (d) 0.0968 101. Solve the following-
RRB JE - 26/05/2019 (Shift-III) 144 121 132
× × =?
Ans : (d) From given expression, 6 8 484
44 4 0.4 48.4 155
%+ %+ % = % (a) 4 (b)
5 5 5 5 36
48.4 0.484 33 3
= = = 0.0968 (c) (d)
500 5 2 4
RRB NTPC 06.04.2021 (Shift-II) Stage Ist
5 2 6
98. The decimal representation of + - is: 144 121 132
100 5 25 Ans. (c) : · × ×
6 8 484
(a) 0.21 (b) 0.35
(c) 0.51 (d) 0.45 12 11 132 33
= × × =
RRB NTPC 05.02.2021 (Shift-I) Stage Ist 6 8 22 2

Decimal Fractions 65 YCT

 1 1 1 1 0.3
102. Find the value of + + + .... + =
1.4 4.7 7.10 47.50 103
49 47 = 0.3 × 10 −3
(a) (b)
50 150 = 3 × 10 −1 × 10 −3
(c)
47
(d)
49 ? = 3 × 10 −4
50 150 4
RRB NTPC 16.02.2021 (Shift-II) Stage Ist
Ans. (d) : 106. Convert 9 in its simple form:
12
1 1 1 1
+ + + ....... + 1 1
1.4 4.7 7.10 47.50 (a) (b)
26 29
Given expression 1, 4, 7, ….47, and 4, 7, 10, …..50 are
in arithmetic series whose difference is 3. In this case 1 1
(c) (d)
sum of given term– 25 27
1  1 1  RRB Group-D – 26/09/2018 (Shift-I)
 −  Ans : (d)
Difference  First term Last term 
4
1 1 1 
=  −  9 = 4× 1 = 1
3  1 50  12 9 12 27
1 49 2
= × 107. 1 inversely proportional to :
3 50 3
49 2 3
= (a) 2 (b)
150 3 5
103. Which of these fractions cannot be reduced 1 2
further? (c) 3 (d)
14/21, 33/43, 18/24, 41/82 2 3
(a) 33/43 (b) 92/24 RRB Group-D – 30/10/2018 (Shift-II)
(c) 18/24 (d) 41/82 2
Ans : (b) 1
RRB JE - 26/05/2019 (Shift-III)
3
Ans : (a)
14 2 33 33 5
= , = =
21 3 43 43 3
18 3 3
= On writing in inverse =
24 4 5
41 1 108. The lowest fractional value of 4.025 =?
=
82 2 161 116
(a) (b)
33 40 20
Hence, it is clear that cannot be reduced further.
43 161 116
6 27 20 (c) (d)
104. Simplify : ÷ ÷ 20 40
27 30 81 RRB Group-D – 30/10/2018 (Shift-II)
(a) 9 (b) 6 Ans : (a) The fractional form of 4.025,
(c) 3 (d) 1
4025
RRB RPF Constable -20/01/2019 (Shift-II) ·
6 27 20 1000
Ans : (d) ÷ ÷ 161
27 30 81 =
6 30 81 6 × 3 × 3 6 40
= × × = = =1 109. Which of the following fractions is not
27 27 20 27 × 2 3 × 2
equivalent to 4/11?
0.3 64 20
105. equals to : (a) (b)
1000 176 55
(a) 3 × 10–4 (b) 3 × 10–6
5 –5 84 32
(c) 3 × 10 (d) 3 × 10 (c) (d)
RRB Group-D – 23/09/2018 (Shift-I) 209 88
0.3 RRB Group-D – 27/09/2018 (Shift-I)
Ans : (a) =?
1000 Ans. (c) From options–
0.3 64 4 20 4
(a) = (b) =
1000 176 11 55 11

Decimal Fractions 66 YCT

 84 32 4 114. Which of the fractions below given is NOT
(c) = 0.401 (d) = 9
209 88 11 equal to ?
Hence, option (c) is not equivalent to 4/11. 17
1 108 27
110. 2 =? (a) (b)
25 221 51
(a) 0.24 (b) 2.4 63 153
(c) 2.004 (d) 2.04 (c) (d)
RRB Group-D – 27/09/2018 (Shift-III) 119 289
1 51 RRB ALP & Tec. (31-08-18 Shift-I)
Ans : (d) 2 = = 2.04 9
25 25 Ans : (a) Given:
111. What fraction of a day equals to 7 minutes and 17
12 second? 9 × 3 27
1 1 =
(a) (b) 17 × 3 51
240 225
9×7 63
1 1 =
(c) (d) 17 × 7 119
200 300
RRB Group-D – 16/10/2018 (Shift-II) 9 × 17 153
=
Ans : (c) The number of hours in a day = 24 17 ×17 289
= 24 × 60 × 60 sec 108 9
7 min 12 sec = (7 × 60 + 12) Hence
221
will not give any equivalent fraction of
17
.
= (420 + 12) = 432 sec
115. How many kilometres are there in one metre?
432 1
The required fraction = = (a) 0.0001 (b) 0.1
24 × 60 × 60 200
(c) 0.001 (d) 0.01
3 3 RRB ALP & Tec. (10-08-18 Shift-III)
112. Simplify : +
1 1 Ans : (c) 1000m = 1km.
7 3
3 7 1
3 4 1m = km. = 0.001 km.
(a) 1 (b) 1 1000
11 11 Hence, one metre has 0.001 km.
3 4
(c) 2 (d) 2
7 7 Type - 6
RRB NTPC 29.03.2016 Shift : 2
3 3 3 3 2
Ans : (b) + = + 116. What will be the value if you multiply by the
1 1 22 22 11
7 3 5
3 7 3 7 reciprocal of − ?
9 21 14
= +
22 22 28 28
(a) (b) −
30 55 55
=
22 2 10
(c) (d) −
15 4 3 153
= =1
11 11 RRB NTPC 21.01.2021 (Shift-II) Stage Ist
113. Find the solution of :– 4/11 + 2/7 + 3/5 5 14
(a) 37/35 (b) 481/385 Ans. (b) : Reciprocal of – · –
(c) 13/35 (d) 37/385 14 5
RRB NTPC 18.01.2017 Shift : 3 2  14  28
4 2 3 ∴ × –  = –
Ans : (b) + + 11  5  55
11 7 5 117. The reciprocal of the sum of the reciprocals of
35 × 4 + 2 × 55 + 3 × 77
= 5/7 and 9/5 is:
385 35 88
140 + 110 + 231 (a) (b)
= 88 45
385
45 88
481 (c) (d)
= 88 35
385 RRB NTPC 27.02.2021 (Shift-I) Stage Ist
Decimal Fractions 67 YCT
 5 9 160x2 – 999x – 160 = 0
Ans. (c) :The sum of reciprocals of and 160x2 – (1024–25)x – 160 = 0
7 5
160x2 – 1024x + 25x – 160 = 0
7 5
= + 32x (5x – 32) + 5 (5x – 32) = 0
5 9 (32x + 5) (5x – 32) = 0
63 + 25 88 32x + 5 = 0 , 5x – 32 = 0
= =
45 45 32x = – 5 , 5x = 32
5 9 −5 32
Hence, the inverse of the sum of reciprocal of and x= , x=
7 5 32 5
45 120. The difference of a fraction and its inverse is
=
88 9
. Then the difference of cubes of the fraction
11
25
118. The sum of A fraction and its inverse is 2 .
and its inverse will be:
66
Find the greater number of the two: 1331 2538
(a) – (b) –
15 5 2538 1331
(a) 1 (b) 1 3996 729
22 6 (c) (d)
20 5 1331 1331
(c) 1 (d) 1 RRB Group-D – 11/10/2018 (Shift-I)
33 11
RRB Group-D – 05/10/2018 (Shift-II) Ans : (c)
1 x 1
Ans : (b) Let the fraction be x and its inverse be . Let the fraction be , then its inverse will be ,
x 1 x
According to the question, According to the question,
1 25 x 1 9
x + = 2 − − − − − (I) − =
x 66 1 x 11
From option (b),
1 9
5 11 ⇒ x− =
Putting the value x = 1 = in equation ( Ι ) , x 11
6 6
11 6 25 On cubing both side,
+ =2 3
6 11 66 1 9 9
x3 −
=   + 3× a 3 − b3 = (a − b)3 + 3ab(a − b)
⇒
121 + 36
=2
25 3
x  11  11 
66 66 729 27
157 25 = +
⇒ =2 1331 11
66 66
25 25 729 + (27 × 121) 729 + 3267
⇒2 =2 = =
66 66 1331 1331
5 1 3996
Hence greatest fraction = 1 ∴ x3 − 3 =
6 x 1331
119. The difference between a positive fraction and 4 5
39 121. How should be added to to obtain ?
its inverse is 6 . Find the fraction. 5 4
160
32 13 1 16
(a) (b) (a) (b)
5 8 −1 20
15 16 9 1.25
(c) (d) (c) (d)
8 5 20 0.8
RRB Group-D – 15/10/2018 (Shift-II) RRB ALP & Tec. (21-08-18 Shift-II)
Ans : (a) Let the positive fraction be x Ans : (c) Let x be added to the number.
1 According to the question,
So, inverse =
x 4 5
According to the question, x+ =
5 4
1 39
x– =6 5 4 25 − 16 9
x 160 x= − , x = , x =
2
x – 1 999 4 5 20 20
= 9
x 2 160 Hence the required number is .
160x – 160 = 999x 20

Decimal Fractions 68 YCT

 125. What is the difference between the biggest and
Type - 7 2 3 4
the smallest fraction among , , and ?
5
3 4 5 6
122. Which of the following fractions should be 1 1
(a) (b)
5 11 30 6
added to to obtain as the sum? 1 1
9 6 (c) (d)
12 20
5 1 RRB NTPC 15.02.2021 (Shift-II) Stage Ist
(a) 1 (b) 1
18 3 2 3 4 5
Ans. (b) : , , ,
5 7 3 4 5 6
(c) 1 (d) 1 For equaling denominator we have to multiply and
15 18
divide each fraction by LCM of 3, 4, 5 and 6 = 60.
RRB NTPC (Stage-II) –13/06/2022 (Shift-II) 2 60 3 60 4 60 5 60
⇒ × , × , × , ×
x 3 60 4 60 5 60 6 60
Ans. (a) Let the fraction to be added is =
y 40 45 48 50
⇒ , , ,
According to the question, 60 60 60 60
5
5 x 11 Hence, biggest fraction =
+ = 6
9 y 6
2
Smallest fraction =
x 11 5 3
= –
y 6 9 5 2 1
Required difference = – =
33 –10 6 3 6
=
18 5 2
126. Find the sum of and .
x 23 2 5
= 10 29
y 18 (a) (b)
7 10
x 5 20 7
or =1 (c) (d)
y 18 7 7
5 11 RRB NTPC 31.01.2021 (Shift-I) Stage Ist
123. Sum of and =?
11 5 5 2 25 + 4
Ans. (b) : + =
146 16 2 5 10
(a) (b)
55 16 29
=
16 110 10
(c) (d)
55 55 127. Find the number obtained by adding the sum
RRB Group-D – 26/09/2018 (Shift-II) and difference of the numbers 3.03 and 2.05.
(a) 0.606 (b) 6.06
5 11
Ans. (a) : + (c) 600.6 (d) 60.06
11 5 RRB NTPC 05.01.2021 (Shift-I) Stage Ist
25 + 121 146
= = Ans. (b) : 3.03 + 2.05 = 5.08
55 55 3.03 – 2.05 = 0.98
1 4 3 ––––––
124. What is the sum of , and + 6.06
3 3 4
––––––
26
(a) (b) 2 3 2
12 128. What should be subtracted from  –  to get
4 3
27 29
(c) (d) –1
12 12 ?
6
RRB NTPC 01.02.2021 (Shift-II) Stage I 2 1
(a) (b) 1
Ans. (d) : From question, 4 4
1 1
1 4 3 4 + 16 + 9 29 (c) (d)
+ + = = 4 3
3 3 4 12 12 RRB NTPC 24.07.2021 (Shift-II) Stage Ist
Decimal Fractions 69 YCT
Ans. (c) : Let, the number x to be subtracted (a) 27 (b) 25
3 2 1 (c) 13 (d) 12
 – –x= − RRB NTPC 23.02.2021 (Shift-I) Stage Ist
4 3 6
 9−8 1 Ans. (a) : If number ·x
 −x = − 42 − x 5
 12  6
Then =
1 1 45 − x 6
 −x = − 252 – 6x = 225 – 5x
 12  6
1 1 1+ 2 252 – 225 = 6x – 5x
+ =x⇒ x = 27
12 6 12
Hence the number to be subtracted from the numerator
3 1
x= ⇒ x= 42
12 4 and denominator of the fraction · 27
45
–5
129. What number should be added to to get 132. The difference between the fractions 5 minutes
7 of an hour and 20 seconds of an hour is:
–2 16 28
? (a) (b)
3 180 270
–7 10
(a) (b) 0.7 7
21 21 (c) (d)
9 12
1 7 RRB NTPC 08.01.2021 (Shift-I) Stage Ist
(c) (d)
21 21
Ans. (c) : From question,
RRB NTPC 24.07.2021 (Shift-II) Stage Ist
The fractions 5 minutes of an hour and 20 seconds of
Ans. (c) : From question, an hour
−5 −2 5 20
+? = = h – h
7 3 60 3600
−2  −5  −2 5 5 2 15 − 14 5 2
= −  = + = − = = −
3  7  3 7 7 3 21 60 360
30 − 2
1 =
= 360
21
28
130. What number must be subtracted from both =
360
the numerator and denominator of the fraction
15 3 7 0.7
so as to make it ? = = h
19 4 90 9
(a) 5 (b) 9 1
133. The fraction which, when subtracted from
(c) 6 (d) 3 2
RRB NTPC 22.02.2021 (Shift-I) Stage Ist 3
gives is:
3 4
Ans. (d) : Let the fraction become on subtracting the 1 1
4 (a) (b) −
number x from the numerator and denominator. 4 4
According to the question, 1 1
(c) (d) −
On subtracting x in both numerator and denominator of 3 3
15/19' RRB RPF-SI -12/01/2019 (Shift-III)
15 – x 3 1
= Ans. (b) : Let the fraction be ,
x
19 – x 4
60 – 4x = 57 – 3x According to the question,
1 1 3 1 3 1 1 3−2
x=3 − = ⇒− = − ⇒ − =
Required number x = 3 2 x 4 x 4 2 x 4
131. What number must be subtracted from both 1 1
=−
the denominator and numerator of the fraction x 4
42 5 1
so that it becomes ? Hence, the required fraction is − .
45 6 4

Decimal Fractions 70 YCT

 3 13 19 31 23 According to the question,
134. The value of + - + - =? x 5 7
15 14 21 35 30 + =
8 1 y 3 4
(a) (b)
21 3 x 7 5 21 − 20 1
= − = =
2 12 y 4 3 12 12
(c) (d)
5 35 1
RRB Group-D – 20/09/2018 (Shift-II) Hence, the required fraction is 12 .
Ans : (d) 137. Find the difference between 0.02 and 0.002.
3 13 19 31 23 (a) 0.018 (b) 0.0018
+ − + −
15 14 21 35 30 (c) 1.8 (d) 0.18
(LCM of 15, 14, 21, 35 and 30 is 210) RRB Group-D – 17/09/2018 (Shift-III)
42 + 195 − 190 + 186 − 161 Ans. (a) : The difference of 0.02 and 0.002,
=
210 0.02 × 100 0.002 × 1000
⇒ −
423 − 351 100 1000
⇒
210 2 2
⇒ −
72 12 100 1000
⇒ =
210 35 20 − 2
⇒
12 1000
Hence, the required value is .
35 18
⇒ = 0.018
1 1000
135. The subtracted value of a fraction from is Hence, the required difference is 0.018.
6
1 138. Which of the following fraction will be
. Find the fraction. 3 5
13 subtracted from to give the result ?
7 5 4 12
(a) (b) 1 2
78 13 (a) (b)
1 11 3 8
(c) (d)
7 39 1 2
RRB Group-D – 03/10/2018 (Shift-III) (c) (d)
6 3
x RRB Group-D – 19/09/2018 (Shift-III)
Ans : (a) Let the fraction be ,
y 1
According to the question, Ans. (a) : Let the fraction be ,
x
1 x 1 According to the question,
= – =
6 y 13 3 1 5
− =
x 1 1 4 x 12
= –
y 6 13 1 5 3
− = −
x 13 − 6 x 12 4
= 1 20 − 36
y 78 − =
x 7 x 48
= 1 −16
y 78 − =
7 x 48
Hence, the required fraction is . 1 1
78
=
7 5 x 3
136. The sum of two fractions is . If one is , find 1
4 3 Hence, the required fraction is .
the another. 3
1 2 10 11
(a) (b) 139. What should be added to to get ?
5 1 11 10
1 1 21 1
(c) (d) (a) (b)
12 10 110 −1
RRB Group-D – 18/09/2018 (Shift-II) 1 2
x (c) (d)
Ans. (c) : Let the required fraction be , 55 11
y RRB Group-D – 20/09/2018 (Shift-I)
5 Ans. (a) : Let the number to be added is x.
And the another fraction is given = ,
3 According to the question,

Decimal Fractions 71 YCT

 10 11 ⇒ 3x +7 = 4 × 3
+x= ⇒ 3x + 7 = 12 ⇒ 3x = 12 – 7 ⇒ 3x = 5
11 10
11 10 121 − 100 21 5  2
x= − = = ⇒ x = = 1 
10 11 110 110 3  3
21 2
Hence the required number is . Hence, the required fraction is 1 .
110 3
3 3 5
140. What should be added to 5 to get 8 ? 143. The difference between two fractions is . The
5 7 6
99 96
(a) (b) 3
35 35 smaller one is . Find the other.
4
99 94
(c) (d) 1 19
33 35 (a) (b)
RRB Group-D – 25/09/2018 (Shift-III) 12 24
Ans. (a) : Let the required number be x. 19 8
(c) (d)
According to the question, 12 10
3 3 RRB Group-D – 22/10/2018 (Shift-II)
5 +x =8
5 7 Ans : (c) Let the other fraction be x.
3 3 59 28 According to the question,
x · 8 −5 = − 3 5
7 5 7 5 x− =
295 − 196 99 4 6
= =
35 35 5 3
⇒x= +
99 6 4
Hence, the required number is
35 38 19
x= =
7 24 12
141. The sum of two fractions is . One of the
6 19
3 Hence, the other fraction is .
fraction is . Find the other. 12
4 5 3
4 5 144. The value of + =?
(a) (b) 3 5
12 12 15 8
4 1 (a) (b)
(c) (d) 8 15
2 12 4 8
RRB Group-D – 26/09/2018 (Shift-III) (c) 2 (d)
Ans : (b) Let the other fraction is x. 15 8
According to the question, RRB Group-D – 22/10/2018 (Shift-II)
3 7 7 3 Ans : (c) From given expression,
⇒ x+ = ⇒x = − 5 3
4 6 6 4 ⇒ +
14 − 9 5 3 5
⇒x= = 25 +9
12 12 =
5 15
Hence, the required fraction is . 34 4
12
= =2
7 15 15
142. A fraction when added to , gives 4. Find the
3 25 15
fraction. 145. The difference of and =?
12 8
2 11
(a) 1 (b) 10 7
3 2 (a) (b)
1 2 24 13
(c) − (d) 10 5
2 3 (c) (d)
RRB Group-D – 28/09/2018 (Shift-I) 4 24
Ans : (a) Let the required fraction be x. RRB Group-D – 06/12/2018 (Shift-II)
According to the question, 25 15
x 7 Ans. (d) The difference of and ,
⇒ + =4 12 8
1 3
3x + 7 25 15 50 − 45 5
⇒ =4 − = =
3 12 8 24 24

Decimal Fractions 72 YCT

 25 5 149. What is the fraction which, when subtracted
146. To get , should be multiplied by: 3 2
3 12 from , gives ?
(a) 10 (b) 20 4 5
4 5 1 7
(c) (d) (a) - (b)
5 4 1 20
RRB Group-D – 05/12/2018 (Shift-II) 1 3
Ans. (b) Let the required number be x. (c) (d)
According to the question, 20 10
RRB Group-D – 08/10/2018 (Shift-III)
5 25
×x = x
12 3 Ans : (b) Let the fraction be .
y
x
=5 According to the question,
4 3 x 2
x = 20 − =
147. The square root of a positive fraction, when 4 y 5
1 x 3 2
added to 1, is 3 . Find the fraction. ⇒ = −
4 y 4 5
1 1 x 15 − 8
(a) 2 (b) 6 ⇒ =
4 4 y 20
1 1
(c) 5 (d) 3 x 7
16 16 =
RRB Group-D – 02/11/2018 (Shift-I) y 20
Ans. (c) 150. What should be added to 3/5 to get 5/4?
x 15 13
Let the fraction be = (a) (b)
y 20 20
According to the question, 2 1.25
(c) (d)
x 1 −1 0.6
+1 = 3 RRB Group-D – 05/10/2018 (Shift-III)
y 4
Ans. (b) Let the required number be x.
x 13 According to the question,
= −1
y 4 5 3
= +x
x 9 4 5
=
y 4 5 3
– =x
x 81 x 1 4 5
= , =5 25 − 12
y 16 y 16 =x
11 7 20
148. The difference between and =? 13
12 8 x=
1 4 20
(a) (b) 13
4 4 Hence, the required number is .
4 1 20
(c) (d) 151. When A fraction is subtracted from 1/5 gives
24 24 1/12. Find the fraction.
RRB Group-D – 11/12/2018 (Shift-III)
1 11
11 7 (a) (b)
Ans : (d) The difference between and 7 30
12 8
11 7 7 5
= − (c) (d)
12 8 60 12
88 − 84 RRB Group-D – 04/10/2018 (Shift-I)
= x
96 Ans. (c) Let the fraction be .
y
4
= According to the question,
96
1 x 1
1 − =
= 5 y 12
24
1 1 1 x
Hence, the required difference is . − =
24 5 12 y

Decimal Fractions 73 YCT

 12 − 5 x 3 1
= (c) (d)
60 y 4 9
RRB ALP & Tec. (14-08-18 Shift-I)
x 7
= x
y 60 Ans : (b) Let the fraction be .
y
152. In which fraction, when 5/16 is added gives 1? According to the question,
11 13
(a) (b) 1 x 1
32 2 − =
3 y 12
22 6
(c) (d) x 1 1 4 −1 3 1
32 8 = − = = =
RRB Group-D – 19/09/2018 (Shift-I) y 3 12 12 12 4
Ans : (c) Let the fraction be x. x 1
=
5 5 y 4
x + = 1, x = 1–
16 16 156. Which of the fractions given below, when
11 2 × 11 22 5
x= , x= = added to , gives 1?
16 2 × 16 32 8
22 6 5
Hence, the require fraction is . (a) (b)
32 24 2
153. What is the fraction which, when subracted 6 6
(c) (d)
1 2 16 3
from , gives ?
2 3 RRB ALP & Tec. (09-08-18 Shift-II)
1 1 Ans : (c) Let the fraction be x.
(a) (b) − According to the question,
3 3
1 1 5
(c) − (d) + x =1
6 6 8
RRB ALP & Tec. (20-08-18 Shift-I) 5 3
x=1– x=
x 8 8
Ans : (c) Let the fraction be . 3× 2
y x=
According to the problem, 8× 2
6
1 x 2 x 1 2 x=
− = ⇒ = − 16
2 y 3 y 2 3 6
Hence the required fraction is = .
x −1 16
=
y 6
2 3
Type - 8
154. How much should be added to to obtain ?
3 2 157. The value of 0.0006697 to three digits of
4 5 decimal will be:
(a) (b) (a) 0.000670 (b) 0.00669
9 6
(c) 0.001 (d) 0
1 1.5 RRB RPF Constable -22/01/2019 (Shift-I)
(c) (d)
−1 6 Ans : (c) The value of 0.0006697 till three digits of
RRB ALP & Tec. (17-08-18 Shift-I) decimal = 0.001,
Ans : (b) Let the number to be added is x. After decimal if the right digit is 5 or more than 5, then
we add 1 to the left digit.
According to the question,
15
2 3 158. Which fraction is not equal to ?
+x = 23
3 2 105 75
3 2 9−4 5 (a) (b)
x= − = = 162 115
2 3 6 6 45 30
1 1 (c) (d)
155. A fraction, when subtracted from gives . 69 46
3 12 RRB RPF-SI -12/01/2019 (Shift-I)
The fraction is: Ans : (a) From options–
5 1 105 35 75 15
(a) (b) (a) = (b) =
12 4 162 54 115 23
Decimal Fractions 74 YCT
 45 15 30 15 164. Find the value of x.
(c) = (d) = 144 14.4
69 23 46 23 =
15
0.144 x
Hence, it is clear that option (a) is not equal to . (a) 0.0001 (b) 0.0144
23 (c) 0.1 (d) 0.01
159. 0.065 × 0.4 = ? RRB Group-D – 16/10/2018 (Shift-I)
(a) 0.26 (b) 0.026 Ans. (b) : Given expression,
(c) 2.6 (d) 0.0026 144 14.4
RRB RPF-SI -11/01/2019 (Shift-I) =
0.144 x
Ans : (b) Given,
0.065 × 0.4 = 0.026 144 × x = 14.4 × 0.144
160. Find the value of 0.1404 ÷ 0.06 = ? 14.4 × 0.144
x=
(a) 0.234 (b) 2.34 144
(c) 234 (d) 23.4 144 × 0.144
RRB RPF Constable -18/01/2019 (Shift-I) x=
144 × 10
Ans :(b) Given, x = 0.0144
0.1404 ÷ 0.06
165. If x is integer 0.80000, then what is interval of
0.1404 × 10000 1404 x?
= = = 2.34
0.06 × 10000 600 (a) 0.79995 < x ≤ 0.80005
161. Find the sum of the place value of 5 and 4 in (b) 0.799905 ≤ x < 0.800005
6 6 (c) 0.799995 ≤ x < 0.800005
and respectively.
8 25 (d) 0.79995 ≤ x < 0.80005
8 99 RRB Group-D – 30/10/2018 (Shift-I)
(a) (b) Ans : (c)
100 100
The required interval of x = 0.799995 ≤ x < 0.800005
9 88
(c) (d) 0.7
100 100 166. If = -0.2 , then c = ?
RRB Group-D – 28/09/2018 (Shift-III) 1 - 6c
(a) 0.8 (b) 0.5
6
Ans : (c) = 0.75 (c) 0.75 (d) 0.075
8 RRB Group-D – 20/09/2018 (Shift-I)
5 Ans. (c) : Given,
The place value of 5, in 0.75 = 0.05 =
100 0.7
= −0.2
6 1 − 6c
and, = 0.24
25 −0.2 + 1.2c = 0.7
4 1.2 c = 0.9
The place value of 4, in 0.24 = 0.04 =
100 0.9
So, the required sum of both values c=
1.2
5 4 9 c = 0.75
= + =
100 100 100 167. x is written as 15.84, to two digits of decimal.
162. The whole value of 0.008594 to three digits of Which of the following is true?
decimal will be? (a) 15.835 < x ≤ 15.845
(a) 0.008 (b) 0.009 (b) 15.835 < x < 15.845
(c) 0.00860 (d) 0.00859 (c) 15.835 ≤ x ≤ 15.845
RRB Group-D – 08/10/2018 (Shift-II) (d) 15.835 ≤ x < 15.845
Ans : (b) As we know :- After decimal if the right digit RRB Group-D – 09/10/2018 (Shift-I)
is 5 or more than 5, then we add 1 to the left digit. Ans. (d) : Analyzing option (d),
Hence, the whole value of 0.008594 to the three digits 15.835 is less than x, and 15.835 is written to two digits
of decimal will be 0.009. of decimal as 15.84 (approx). While 15.845 will be
163. x and y, given correct to 2 decimal place, are definitely greater.
given as 4.51 and 2.48 respectively. What is the 168. If x is 0.70000, to five digits of decimal, then
upper limit of the value of x + y? (The value is interval of x will be:
correct to the two digits of decimal.) (a) 0.6995 ≤ x < 0.70005
(a) 7.000 (b) 6.995 (b) 0.699995 ≤ x < 0.700005
(c) 7.010 (d) 6.990 (c) 0.699905 ≤ x < 0.700005
RRB Group-D – 12/10/2018 (Shift-III) (d) 0.69995 < x ≤ 0.70005
Ans : (a) x + y = 4.51 + 2.48 = 6.99 RRB Group-D – 10/10/2018 (Shift-III)
Hence, the nearest upper limit for the value of (x + y) Ans : (b) If x is 0.70000, to five digits of decimal,
that is 6.99 = 7.000. Then, 0.699995 < x < 0.700005 is correct.

Decimal Fractions 75 YCT

 65
169. The least value of x which makes an Ans : (a) 484 = 48.4
x - 14 4.84 x
integer, is: ⇒ x × 484 = 48.4 × 4.84
(a) 1 (b) –51
(c) 79 (d) –1 484 × 484
⇒ x=
RRB Group-D – 26/10/2018 (Shift-III) 484 ×1000
Ans : (b) From question, Hence, x = 0.484
Putting the value of options in the place of x. 174. x and y, are given correct to the one digit of
65 65 decimal, and written as 6.2 and 1.3
(a) = = − 5 (Integer) x
1−14 −13 respectively. What is the upper limit of ?
65 65 y
(b) = = − 1 is also an integer for which (a) 4.96 (b) 5
−51−14 −65
the value of x is the least. (c) 4.77 (d) 5.05
RRB Group-D – 04/10/2018 (Shift-I)
65 65
(c) = = 1 (Integer) x 6.2
79 −14 65 Ans. (b) = = 4.76
65 65 y 1.3
(d) = = − 4.33 (Non-Integer) x
−1−14 −15 Hence, the value of upper limit of is 5.
Hence, it is clear that the least required value of x is -51 y
144 175 175. 1.008 = ?
170. The product of and will be = ? 1 3
100 216 (a) 1 (b) 1
7 14 125 25
(a) (b) 2 2
12 3 (c) 1 (d) 1
7 7 25 125
(c) (d) RRB Group-D – 01/10/2018 (Shift-II)
6 3
RRB Group 'D' 07/12/2018 (Shift-I) Ans. (a) : 1.008 = ?
1008 504 252 126 1
Ans : (c)
144 175
× ⇒ = = = =1
100 216 1000 500 250 125 125
7 1
= Hence, the value of 1.008 is 1 .
125
6
171. x and y, are given correct to the two digits of 176. If X = 63.5535 , find the value of X.
decimal, are written as 3.57 and 3.42 13.05
respectively. What is the upper limit for x + y ? (a) 4.48 (b) 4.87
(a) 7.000 (b) 7.010 (c) 4.46 (d) 4.28
(c) 6.990 (d) 6.995 RRB Group-D – 23/09/2018 (Shift-II)
RRB Group-D – 23/10/2018 (Shift-I) 63.5535
Ans. (a) : According to the question, Ans : (b) X=
13.05
x and y are correct to the two digits of decimal.
6355.35
x = 3.57 and y = 3.42, X= = 4.87
then, x + y = 3.57 + 3.42 = 6.99 1305
hence, the upper limit of x + y = 7.000 Hence, the value of X is 4.87
172. x and y, are given correct to the two digits of 177. If 2334/33.1 = 261, then 23.34/3.31 = ?
decimal, are written as 2.51 and 3.50 (a) 0.261 (b) 2.61
respectively. What is the lower limit for x + y ? (c) 26.1 (d) 261
(a) 6.010 (b) 5.995 RRB NTPC 18.04.2016 Shift : 3
(c) 6.000 (d) 5.990 Ans : (c) Given,
RRB Group-D – 15/10/2018 (Shift-II) 2334
= 261........(1)
Ans : (c) According to the question, 33.1
x = 2.51 and y = 3.50 23.34 2334
then, Q =
3.31 331
x + y = 2.51 + 3.50 = 6.01 2334
So the lower limit for x + y is 6.000 =
33.1× 10
173. Find the value of x.
2334 1
484 48.4 = ×
= 33.1 10
4.84 x 261
(a) 0.484 (b) 0.00484 = {from equation (1)}
(c) 0.0484 (d) 4.84 10
RRB Group-D – 08/10/2018 (Shift-III) = 26.1

Decimal Fractions 76 YCT

178. If 23 × 19 = 437, then 0.0437 ÷ 1.9 = ? Ans : (b) From the given fractions,
(a) 0.0023 (b) 2.3 7 11
(c) 0.023 (d) 0.23 = 0.58 = 0.68
12 16
RRB ALP & Tec. (21-08-18 Shift-I)
From options–
Ans : (c) Given,
1 5
23×19 = 437 (a) = 0.50 (b) = 0.62
According to the question, 2 8
0.0437 0.0437 × 10000 7
(c) = 0.87
3
(d) = 0.37
=
1.9 1.9 × 10000 8 8
23 × 19 Hence, option (b) is 0.62, which is greater than 0.58 and
= smaller than 0.68.
19 × 1000
23 183. Which of the following is correct?
= = 0.023 9 13 9 13
1000 (a) ≤ (b) >
16 24 16 24
179. If 17 × 29 = 493. How much is 1700 x 0.0029 ?
9 13 9 13
(a) 0.493 (b) 0.0493 (c) = (d) <
(c) 4.93 (d) 49.3 16 24 16 24
RRB Group-D – 19/09/2018 (Shift-III) RRB Group-D – 17/09/2018 (Shift-I)
Ans. (c) : 17×29 = 493, lees 1700×0.0029 · ? Ans : (b) From options,
9 13
⇒ 1700×0.0029 (a) ≤ = 0.56 ≤ 0.54 (wrong)
⇒ 17×100×0.0029 16 24
⇒ 17×0.29 9 13
(b) > = 0.56 > 0.54 (right)
⇒ 4.93 16 24
180. If 493 ÷ 29 = 17, then 4.93÷ 0.0017 = ? 9 13
(c) = = 0.56 = 0.54 (wrong)
(a) 290 (b) 0.29 16 24
(c) 2.9 (d) 2900 9 13
(d) < = 0.56 < 0.54 (wrong)
RRB ALP & Tec. (13-08-18 Shift-I) 16 24
Ans : (d) Given, 184. Find the smallest of the following decimals.
493 ÷ 29 = 17 , (a) 0.1 × 0.1 × 0.1 (b) 0.03 / 3
So, (c) 0.01 / 2 (d) 0.1 × 0.02 × 0.2
4.93 RRB NTPC 05.04.2016 Shift-1
4.93 ÷ 0.0017 = Ans : (d) From options–
0.0017
(a) 0.1 × 0.1 × 0.1 = 0.001
4.93×10000 49300
= = (b) 0.03 / 3 = 0.01
0.0017 ×10000 17 (c) 0.01 / 2 = 0.005
= 2900 (d) 0.1 × 0.02 × 0.2 = 0.0004
Hence option (d) is the smallest.
181. 23 × 31=713. How much is 0.0713 ÷ 3.1?
185. Find the smallest of the following decimals.
(a) 0.0023 (b) 0.23
(a) 0.2 × 0.2 × 0.2 (b) 0.02 / 3
(c) 0.023 (d) 2.3
(c) 0.01 / 2 (d) 0.1 × 0.02 × 2
RRB ALP & Tec. (13-08-18 Shift-III) RRB NTPC 31.03.2016 Shift : 2
Ans : (c) Given, Ans : (d) From options–
23×31 = 713 (a) 0.2 × 0.2 × 0.2 = 0.008
So, 0.02
0.0713 (b) = 0.0067
0.0713 ÷ 3.1 = 3
3.1
0.01
0.0713×10000 713 (c) = 0.005
= = 2
3.1×10000 31000
(d) 0.1 × 0.02 × 2 = 0.004
= 0.023 Hence, it is clear that option (d) is the smallest.
186. Find the fraction which is as much greater than
4 5
Type - 9 as it is less than :
7 6
182. Which of the following fractions is greater than 59 84
(a) (b)
7/12, and smaller than 11/16? 84 59
(a) 1/2 (b) 5/8 58 59
(c) (d)
(c) 7/8 (d) 3/8 84 85
RRB JE - 27/06/2019 (Shift-I) RRB ALP & Tec. (10-08-18 Shift-I)
Decimal Fractions 77 YCT
Ans : (a) Let the fraction is x. x −1+ 6 5
According to the question, =
x 4
4 5 4x + 20 = 5x
<x>
7 6 x = 20
Then,
x − 1 19
Sum of both fractions Hence, fraction ⇒
x ( Middle fraction ) = x 20
2
4 5 24 +35 190. Convert 25 grams to kilogram and express the
+
x= 7 6 = 42 = 59 answer as a fraction.
2 2 84 1 1
187. The product of two numbers is 0.432. One of (a) kg (b) kg
the number is 1.6. What is the other number? 40 400
(a) 2.7 (b) 0.027 1 1
(c) kg (d) kg
(c) 0.27 (d) 27 4000 4
RRB ALP & Tec. (10-08-18 Shift-I) RRB Group-D 06/09/2022 (Shift-I)
Ans : (c) Ans. (a) : 1000 gm = 1kg
Prouduct of both numbers
The required number = 1
First number 1gm = kg
1000
0.432
= so,
1.6
25
= 0.27 ∴ 25 gm = kg
1000
188. Which of the following is true?
29 53 29 43 1
(a) = (b) = = kg
6 12 6 12 40
29 43 29 43 191. If we add 1 to the numerator and subtract 1
(c) > (d) < from the denominator of a given fraction, it
6 12 6 12
RRB ALP & Tec. (09-08-18 Shift-I) 2
becomes 1. It becomes if 1 is added to the
Ans : (c) From options– 3
29 53 denominator of the given fraction while the
(a) = ⇒ 4.83 = 4.41 (false) numerator is left unchanged. The fraction
6 12 originally given is:
29 43
(b) = ⇒ 4.83 = 3.58 (false) 5 3 1 6
6 12 (a) (b) (c) (d)
29 43 8 8 8 8
(c) > ⇒ 4.83 > 3.58 (true) RRB GROUP-D – 15/09/2022 (Shift-III)
6 12
29 43 x
(d) < ⇒ 4.83 < 3.58 (false) Ans. (d) : Let the fraction be
6 12 y
Hence, option (c) is correct. According to first condition,
x +1
Type - 10 y −1
=1

x+1=y–1
189. The numerator of a fraction is one less than the
denominator. If 6 is added to the numerator, x – y = –2 ....... (i)
5 According to second condition,
the fraction will be equal to Find the x 2
4 =
fraction. y +1 3
20 19 3x = 2y +2
(a) − (b)
21 20 3x – 2y = 2 ........ (ii)
21 20 On multiplying by 3 in eq. (i) and substracting eq. (ii) -
(c) − (d)
20 21 –y = –8
RRB Group-D 30/08/2022 (Shift-I) ∴y=8
Ans. (b) : Let, denominator be x x = –2 + 8 [ ∴ From eq. (i)]
then, Numerator = x – 1 x = 6
∴ Fraction = x – 1/x x 6
Hence the original fraction = =
According to the question, y 8

Decimal Fractions 78 YCT

192. Which fraction bears the same ratio to 194. The numerator of a fraction is 2 less than the
1 3 5 denominator. If the numerator is multiplied by
as does to ? 2 and the denominator is multiplied by 3, then
27 11 9
2
1 1 the fraction becomes . The fraction is:
(a) (b) 9
99 27
5 3
1 1 (a) (b)
(c) (d) 7 5
55 15 7 1
RRB NTPC 03.02.2021 (Shift-II) Stage Ist (c) (d)
9 3
x RRB NTPC 28.12.2020 (Shift-II) Stage Ist
Ans. (c) : Let the fraction =
y Ans. (d) : The numerator of fraction = x
According to the question- Denominator = x + 2
x 1 According to the question,
:
y 27 x× 2 2
=
27x : y ...(i) 3( x + 2) 9
3 5 x 1
: =
11 9 3x + 6 9
27 : 55 ....(ii) 9x = 3x + 6
On comparing eqn (i) and (ii),
x=1 , y = 55 x =1
1 x 1
Hence, the fraction = Fraction = =
55 x + 2 3
193. What smallest fraction should be added to 195. The sum of the numerator and denominator of
2 7 9 1 a fraction is 11. If the numerator is decreased
3 + 6 + 4 + 5 + 7 to make the sum a 1
3 12 36 12 by 1, the fraction becomes . Find the
whole number? 4
fraction.
7 11
(a) (b) 2 3
12 12 (a) (b)
9 8
5 13
(c) (d) 4 5
12 12 (c) (d)
RRB NTPC 28.01.2021 (Shift-I) Stage Ist 7 6
RRB NTPC 31.01.2021 (Shift-II) Stage Ist
Ans. (c) : From question,
x
2 7 9 1 Ans. (b) : Let fraction =
3 +6 + 4 +5+7 y
3 12 36 12
x+y =11 ------- (i)
2 7 9 1
= + + + + (3 + 6 + 4 + 5 + 7 ) x −1 1
3 12 36 12 =
y 4
24 + 21 + 9 + 3
= + 25 4x-y =4 ---------- (ii)
36
From equation (i) + equation (ii)
57 5x=15
= + 25
36 x=3
From option (c), y=8 (From equation (i)
5 57 x 3
+ + 25 Hence, fraction = =
12 36 y 8
15 + 57
= + 25 1
196. Find out the fraction which when add to get 2?
36 2
72 1 1
= + 25 (a) (b)
36 2 –1
= 2 + 25 = 27 3 5
(c) (d)
Hence, the sum obtained by adding 5/12 will become a 2 3
whole number. RRB NTPC 31.01.2021 (Shift-II) Stage Ist
Decimal Fractions 79 YCT
 x x → Numerator
Ans. (c) : Let the fraction is Ans. (b) : Let original fraction =
y y → Denominator
According to the question,
According to the question,
1 x
+ =2 x × 130
2 y
100 = 3
x 1
= 2− 65 15
y 2 y×
100
x 3
= 130x 3
y 2 =
3 65y 15
Hence, the fraction will be . x 1
2 =
197. The numerator of a fraction is less than its y 10
denominator by 2. If we subtract 2 from the
numerator and add 2 to the denominator, then 200. How do you show 48% as a fraction?
the new fraction is 1/3 what is the original 10 11
fraction? (a) (b)
(a) 5/7 (b) 5/9 25 25
(c) 1/3 (d) 3/7 1 12
RRB NTPC 01.03.2021 (Shift-I) Stage Ist (c) (d)
25 25
Ans. (a) : Let numerator = x–2 RRB NTPC 23.07.2021 (Shift-II) Stage Ist
denominator = x
According to the question, 48 12
Ans. (d) : 48% = =
(x − 2) − 2 1 100 25
=
x+2 3 201. Which of the following fractions does NOT lie
x−4 1 7 3
= between and ?
x+2 3
3(x – 4) = (x + 2) 18 5
3x –12 = x+2 1 2
2x = 14 (a) (b)
x = 7 2 5
x−2 7−2 5 5 1
Original fraction = = = (c) (d)
x 7 7 12 3
4 RRB NTPC 08.04.2021 (Shift-I) Stage Ist
198. % is equivalent to which of the following
5 7 3
fractions? Ans. (d) : Number between and
1 1 18 5
(a) (b)
25 125 7 3
1 4 = 0.39 and = 0.6
(c) (d) 18 5
725 125
1
RRB NTPC 02.03.2021 (Shift-II) Stage Ist From option (d) = 0.33
3
4 4 1 1
Ans. (b) : % = × = Hence, option (d) does not lie between 0.39 and 0.6.
5 5 100 125
1 202. The numerator of a fraction is 5 less than its
Hence required fraction = denominator. If 2 is subtracted from the
125 numerator and 2 is added to the denominator,
199. If the numerator of a fraction is increased by the fraction becomes 2/5 find the original
30% and its denominator is decreased by 35%, fraction.
3
the value of the fraction becomes . Find the 9 11
15 (a) (b)
original fraction. 11 13
3 1 5 8
(a) (b) (c) (d)
10 10 7 13
1 3 RRB NTPC 30.01.2021 (Shift-I) Stage Ist
(c) (d)
5 5 Ans. (d): Let numerator = a
RRB NTPC 01.02.2021 (Shift-I) Stage Ist denominator = a + 5
Decimal Fractions 80 YCT
According to the question, 20
x×
a−2 2 100 = 5
= 40
a +5+ 2 5 y× 6
5a – 10 = 2a + 14 100
x 5
3a = 24 ⇒ a = 8 =
2× y 6
a 8
∴ Original fraction = = x 5
a + 5 13 =
y 3
203. Three friends arranged a party. Tanveer paid
x 5
2/3 as much as Yusuf paid. Yusuf paid 1/2 as Hence original fraction = =
much as Sachin paid. The fraction of the total y 3
expenditure by Yusuf was. 206. If 3 is added to the numerator and the
7 5 10
(a) (b) denominator of a fraction, it becomes . And
11 11 11
if 4 is subtracted from the numerator and the
3 2 3
(c) (d) denominator, then it becomes . What is the
11 11 4
RRB NTPC 08.01.2021 (Shift-I) Stage Ist fraction?
Ans. (c) : Tanveer Yusuf Sachin 7 6
(a) (b)
2 : 3 : 8 13
1 : 2 3 3
(c) (d)
2 : 3 : 6 4 5
RRB RPF Constable -25/01/2019 (Shift-III)
3 3
∴Total expenditure by Yusuf = = x
( 2 + 3 + 6 ) 11 Ans : (a) Let the fraction is
y
204. A tennis player won 5 matches, lost 12 matches According to the question,
and draw 3 matches in his career. The fraction x + 3 10
of matches which lost in his career is. =
y + 3 11
12 2 ⇒ 11x + 33 = 10y + 30
(a) (b)
5 5 ⇒ 11x − 10y = −3......(i)
1 3
(c) (d) x−4 3
5 5 Again, =
y−4 4
RRB NTPC 29.12.2020 (Shift-II) Stage Ist
⇒ 4x – 16 = 3y – 12
Ans. (d) : Number of matches won by the player · 5 ⇒ 4x – 3y = 4 ...............(ii)
Number of matches lost by the player = 12 From equation (i) and (ii)–
Match draw · 3 x = 7 and y = 8
Number of total matches · 5 + 12 + 3 = 20 7
Hence, the required fraction is .
12 3 8
Hence, fraction of the lost matches = = 207. The difference between 3/8 and another smaller
20 5
number is 1/5. Find another number.
205. If the numerator of a fraction is decreased by 3 2
80% and the denominator of the fraction is (a) (b)
40 3
decreased by 60%, then the resultant fraction
7 8
5 (c) (d)
is . What is the original fraction? 40 15
6
RRB Group-D – 06/12/2018 (Shift-II)
7 3 Ans. (c) : Let the another smaller number is x.
(a) (b)
3 5 According to the question,
5 6 3 1
(c) (d) −x =
3 5 8 5
RRB NTPC 15.02.2021 (Shift-I) Stage Ist 1 3
−x = −
x 5 8
Ans. (c) : Let original fraction is 8 − 15
y −x =
According to the question, 40

Decimal Fractions 81 YCT

 −7 210. 5/12 of a number is 3/4. What is the number?
−x = 1 7
40 (a) 3 (b) 1
7 5 5
x= 4 5
40 (c) 1 (d) 1
7 5 16
Hence, another smaller number is option (c) = . RRB Group-D – 10/12/2018 (Shift-I)
40
208. The denominator of a fraction exceeds 5 by its Ans. (c) : Let the number is x.
numerator. If the numerator is multiplied by 4 According to the question,
and the denominator is multiplied by 3, then 5 3
x× =
1 12 4
the fraction becomes . What is the original
2 9
⇒x=
fraction. 5
3 2 4
(a) (b) x =1
8 7 5
4 1 211. The sum of three fractions is 5. One of them is
(c) (d)
9 6 1 3
1 , and the difference of two others is . Find
RRB Group-D – 27/11/2018 (Shift-III) 2 4
Ans. (a) the greatest of the three.
x 1 1
Let the numerator is x, then the fraction = (a) 2 (b) 2
x +5 4 8
According to the question, 1 7
(c) 2 (d) 1
x×4 1 2 8
=
(x + 5)×3 2 RRB Group-D – 09/10/2018 (Shift-II)
4x 1 Ans. (b) : Let other fractions are x and y.
= According to the question,
3x + 15 2 1
8x = 3x + 15 x + y +1 = 5
5x = 15 2
7
x=3 ⇒ x+y= ............(i)
x 3 3 2
Hence, the required fraction is = = 3
x +5 3+5 8 and x−y= .............(ii)
4
209. If 2 is added to the square of a positive fraction
Subtracting equation (ii) from equation (i),
1
the value 4 is obtained. Find the fraction. 7
4 x+y=
2
3 1
(a) 2 (b) 1 3
4 4 x−y=
4
1 1
(c) 2 (d) 1 − + −
4 2 7 3
RRB Group-D – 15/11/2018 (Shift-II) 2y = −
2 4
Ans : (d) Let the fraction is x.
11
According to the question, 2y =
1 4
x2 + 2 = 4 11
4 y=
17 8
x +2=
2
Putting the value of y in equation (i),
4
11 7
4 x + 8 = 17
2 x+ =
8 2
4 x 2 = 17 − 8 7 11 17 1
9 x= − = = 2 = 2.125
4 x2 = 9 , x2 = 2 8 8 8
4 Hence it is clear that the greatest of the three fractions is
3 1 1
x = =1 2 .
2 2 8

Decimal Fractions 82 YCT

 1 3 7 5
212. Find the divisor of . 215. If of the weight of a brick is kg, then of
5-2 3 4 8 7
(5 − 2 3) 5+2 3 the weight of the brick will be:
(a) (b) 20 5
12 13 (a) kg (b) kg
21 6
5−2 3 5+2 3
5 15
(c) (d) (c) kg (d) kg
13 12 8 32
RRB Group-D – 05/10/2018 (Shift-III)
RRB ALP & Tec. (14-08-18 Shift-I)
1 Ans : (b) Let the weight of the brick is x kg.
Ans. (b) On rationalizing
5−2 3 According to the question,
1 5+ 2 3 3x 7
= × =
5−2 3 5+ 2 3 4 8
5+2 3 5+2 3 7 4
= = x = ×
25 − 12 13 8 3
4 5x 7 4 5
213. If a rod of length 208 is cut into equal pieces Hence = × ×
5 7 8 3 7
1 5x 5
of length 23 , then the total number of rods =
5 7 6
obtained is: 5 5
(a) 5 (b) 7 Hence of weight of the bricks will be Kg.
(c) 8 (d) 9 7 6
RRB ALP & Tec. (31-08-18 Shift-I) 216. Tapan, Ravi and Trisha shared a cake. Tapan
4 1044 1 2
Ans : (d) Total length of the rod = 208 = had of it, Trisha had of it and Ravi had the
5 5 4 3
According to the question, rest. What was Ravi's share of the cake?
Total length of rod 4 1
The number of rods obtained = (a) (b)
Length of one part 7 12
1044 1044 1 2
(c) (d)
= 5 = 5 6 6
1 116 RRB ALP & Tec. (14-08-18 Shift-II)
23
5 5 1
1044 5 1044 Ans : (b) Tapan’s share =
= × = =9 4
5 116 116
2
3 Trisha’s share =
214. A steel rod of length 20 is cut out from a 3
26
1 1 2 11 1
rod of length 56 . Then what is the remaining Hence, Ravi’s share = 1 −  +  = 1 − =
5  4 3  12 12
length of the rod ? 1
3 1 Hence, Ravi’s share of the cake is = .
(a) 36 (b) 36 12
130 130
11 7
(c) 36
130
(d) 36
130 Type - 11
RRB ALP & Tec. (30-08-18 Shift-II)
3 217. 200 g as a fraction of 1 kg is:
Ans : (c) The cut out length of the rod = 20 1 3
26 (a) (b)
523 10 10
= 2 1
26 (c) (d)
1 281 5 5
Total length of the rod = 56 =
5 5 RRB NTPC 21.01.2021 (Shift-II) Stage Ist
281 523 Ans. (d) : According to the question–
The length of the remaining rod = −
5 26 200 1
200g = kg = kg
7306 − 2615 4691 11 1000 5
= = = 36
130 130 130 Therefore, 200g is a 1/5 part of 1 kg.

Decimal Fractions 83 YCT

218. Which of the following number is closest to Ans. (a) : From question,
zero?
36 9
(a) (1-0.09)2 (b) 1-(0.09)2 0.36 = =
(c) 0.009 (d) (0.09)2 100 25
RRB NTPC 08.04.2021 (Shift-I) Stage Ist 9
The sum of the numerator and the denominator of
Ans. (d) : From the given options- 25
(a) (1 – 0.09)2 = 9 +25 = 34
1 + 0.0081 – 0.18 222. When the numerator of a fraction increases by
= 0.8281 6, the fraction increases by three-fourth. The
(b) 1 – (0.09)2 denominator of the fraction is :
1 – 0.0081 (a) 8 (b) 10
= 0.9919 (c) 12 (d) 6
(c) 0.009 RRB NTPC 13.01.2021 (Shift-II) Stage Ist
(d) (0.09)2
= 0.0081 x
Ans. (a) : If fraction is
Hence, option (d) is closest to zero. y
219. Which of the following fraction falls between x+6 x 3
3 6 ⇒ = +
and ? y y 4
4 7
11 9 x+6 x 3
(a) (b) ⇒ − =
9 10 y y 4
5 9
(c) (d) 6 3
9 11 ⇒ =
RRB NTPC 26.07.2021 (Shift-I) Stage Ist y 4
3 ⇒ y=8
Ans. (d) : The given fractions = 0.75
4 223. How many decimal numbers can be found
6 between 0.225 and 0.227?
and = 0.857
7 (a) 2 (b) Infinite
Now from options-
(c) 1 (d) 226
11
(a) = 1.22 RRB NTPC 03.03.2021 (Shift-II) Stage Ist
9
9 Ans. (b)
(b) = 0.9
10 225 227
0.225 = and 0.227 =
5 1000 1000
(c) = 0.55
9 Infinite decimal number can be found between
9 225 227
(d) = 0.818 and .
11 1000 1000
Q 0.818 lies between 0.75 and 0.85
9 3 6 1
Hence, lies between and 224. What would be the value of part of 1.44.
11 4 7 0.24
220. If 58 out of 100 students in a school are boys, (a) 140 (b) 12
then express the part of the school that consists (c) 166 (d) 6
of boys in decimals. RRB NTPC 29.12.2020 (Shift-II) Stage Ist
(a) 0.5 (b) 0.58
1
(c) 0.8 (d) 0.85 Ans. (d) : 1.44 ×
RRB NTPC 08.02.2021 (Shift-II) Stage Ist 0.24
Ans. (b) : Hence, the part of the school that consists of 144
= =6
58 24
boys in decimals = = 0.58
100 225. How many equivalent fraction can be formed
221. When 0.36 is written in its simplest fractional by any fraction?
form, the sum of the numerator and the (a) Only 2 (b) Only 3
denominator is: (c) Infinite (d) Only 1
(a) 34 (b) 35 RRB NTPC 06.04.2021 (Shift-II) Stage Ist
(c) 33 (d) 32 Ans. (c) : From a given fraction, infinite equivalent
RRB NTPC 09.03.2021 (Shift-II) Stage Ist fraction can be formed.

Decimal Fractions 84 YCT

226. If we increase 50% of the numerator and 80% 2 4 6
of the denominator of a fraction, then what 229. 3 , 6 , 9 are–
fraction of the original will be the new fraction.
(a) Odd (b) Irreducible
7 6 5 5
(a) (b) (c) (d) (c) Equivalent (d) Alike (equal)
9 5 8 6
RRB NTPC 12.01.2021 (Shift-I) Stage Ist RRB Group-D – 20/09/2018 (Shift-II)
x Ans : (c) From given fractions,
Ans. (d) : Let fraction = 2
y = 0.6
According to the question, 3
x × 150 4
= 0.6
Fraction after change ·
y × 180 6
5x 6
· = 0.6
6y 9
5 2 4 6
It is clear that new fraction is of the original fraction. = =
6 3 6 9
227. Sum of numerator and denominator of a Hence, it is clear that all the given fractions are
fraction is 13. Adding 3 and 9 to the numerator Equivalent.
and denominator respectively, the fraction 230. Saniya won 18 games out of 27 games played.
becomes 2/3. What is the product of the
numerator and denominator of the original Calculate the games lost in terms of decimal.
fraction? (a) 0.333 (b) 0.033
(a) 45 (b) 42 (c) 0.50 (d) 0.667
(c) 30 (d) 24 RRB NTPC 12.04.2016 Shift : 1
RRB JE - 25/05/2019 (Shift-II) Ans : (a)
Ans : (b) 27 − 18
Let the numerator is x and the denominator is y. The number of games lost, =
27
So, x + y = 13 ...... (i)
9 1
x +3 2 = = = 0.333
= 27 3
y+9 3
3x + 9 = 2y + 18 231. 0.1, 0.9, 0.01, 0.09, ……., 0.009
3x – 2y = 9 ......... (ii) (a) 0.0001 (b) 0.1010
From equation (i) and (ii), (c) 0.001 (d) 0.0011
x = 7, y = 6 RRB RPF-SI -13/01/2019 (Shift-II)
So, the required product = xy = 7 × 6 = 42 Ans : (c) Given,
228. A cake is shared among five friends. Four of 0.1, 0.9, 0.01, 0.09, .........., 0.009
them get the share of the cake
So, the missing term is 0.001,
1 1 5 1 th
, , , respectively. What is the 5 ’s share When we make pairs of two- two, then the pattern
8 6 12 12
of the cake? showed in blank is 0.001, 0.009.
1 5 60 4
(a) (b) 232. If is equivalent to then the value of x is :
6 24 75 x
1 3 (a) 15 (b) 4
(c) (d)
4 8 (c) 18 (d) 5
RRB Group-D – 17/09/2018 (Shift-I) RRB ALP & Tec. (17-08-18 Shift-III)
Ans : (b) The share of the cake all four get Ans : (d) According to the question,
1 1 5 1 60 4
= + + + =
8 6 12 12 75 x
 6 + 8  6 14 6 7 6 19 4 × 75
= + = + = + = ⇒ x=
 48  12 48 12 24 12 24 60
19 5 ⇒ x=5
Hence, the 5th’s share of the cake = 1 − =
24 24 Hence, the value of x is 5.

Decimal Fractions 85 YCT