01

Percentage
How to change % into fraction 1 1
1 1 1 1 1
= 33 % =8 % = 2% = 80 + 3 % = 83 %
3 3 12 3 50 3 3
20 1 1 1 9 3 1 2
20% = = =25% =7 % = 37 % (iv) Find the % value of
100 5 4 13 13 8 2 3

25 1 1 1 æ 1ö
1 1 1 5 1 = 33 % = çç 33 + 3 ÷
÷%
25% = = = 20% =7 % =62 % 3 3 è ø
100 4 5 14 7 8 2
2 2 2
40 2 1 2 1 2 4 1 = 66 + = 66 %
40% = = =16 % =6 % =57 % 3 3 3
100 5 6 3 15 3 7 7
5
70 7 1 2 1 1 5 3 (v) Find the % value of
70% = = =14 % =6 % =71 % 8
100 10 7 7 16 4 7 7
1 1 1
1 1 1 1 1 = 12 % = 12 +
2 50 1 = 12 % =5% =11 % 8 2 2
16 %= % = 8 2 20 9 9
3 3 6 5 5 1 1
1 1 1 1 =60 + = 60 + 2 = 62 %
=4 % =10% =4% 8 2 2 2
2 100 1 24 6 10 25
14 %= %=
7 7 7 4
(vi) Find the % value of
These are Basic Fraction. 7
How to change the fraction into (i) If I want to know the % value 1 2 2
= 14 % = 14 + %
% 5 1 7 7 7
of then go to
9 9 4 8 1 1
1 1 = 56 + % = 56 + 1 = 57 %
 × 100 = 20%
æ 7 7 7 7
5 5 1 1 1ö
= 11 % = çç11 + 9 ÷
÷%
9 9 è ø 7
1 1 (vii) Find the % value of
 × 100 = 25% 12
4 4 5 5
= 55 %
9 9 1 1 1
50 2 =8 %=8+ %
1 1 12 3 3
 × 100 = = 16 % 3
6 6 3 3 (ii) Find the % value of
8 7 7 1 1
= 56 + = 56 + 2 = 58 %
1 1 100 1 1 1 æ 1ö 12 3 3 3
 × 100 = % = 11 % = 12 % = çç12 + 2 ÷
÷%
9 9 9 9 8 2 è ø 11
3 3 1 1 (viii) Find the % value of
= 36 + = 36 + 1 = 37 % 15
8 2 2 2
The following fractions are generally 1 2 2
used in exams. So, I recommend you 5 =6 %=6+ %
(iii) Find the % value of 15 3 3
to remember these fractions. These 6
fractions are very useful to solve the 11 22
1 2 2 = 66 + %
lengthy questions with in time. = 16 % = 16 + 15 3
6 3 3
1 1 1 1 1 1 1
=50% =9 % =2 % 5 10 = 66 + 7 % = 73 %
2 11 11 40 2 = 80 + 3 3
6 3
9
1 (ix) Find the % value of
Percentage
16
 1 1 1 23 24 1 2 1 1 represents its % result
=6 %=6+ % = – 16 %=
16 4 4 12 12 12 3 6 6 represent original
number/value
9 9 1 1 2
= 54 + = 54 + 2 % = 200% – 8 % = 191 % 2 1
16 4 4 3 3  14 %=
7 7
1 41
= 56 % (v) Find the % value of 2
4 6 means 7 × 14 %=1
7
7 41 42 1
(x) Find the % value of = – 1 5
40 6 6 6  62 %=
2 8
1 1 1 2 1 1
=2 %=2+ % = 700% – 16 % = 683 % means 8 × 62 %=5
40 2 2 3 3 2
7 æ 7ö 1 1 3
= çç14 + 2 ÷
÷ % = 17 % How to change % into fraction  37 %=
40 è ø 2 2 8
whose % value is more than 100%
(i) Find the fraction value of 1
How to change the fraction means 8 × 37 %=3
1 2
whose % value is more 157 %
7
than 100%
1 1
7 157 % = 100% + 57 % QUESTIONS BASED ON FRACTION
(i) Find the % value of 7 7
5 1
4 11 1. If 37 % of a number is added
7 5 2 =1+ = 2
 + 7 7
5 5 5 (ii) Find the fraction value of with itself then result becomes
 100% + 40% 1320. Find the original number.
2
 140% 616 % Detailed Method :
3
35 Let the original number be x
(ii) Find the % value of 2 2 According to the question,
8 616 % = 600% + 16 %
3 3 1
35 32 3 x + x × 37 % = 1320
= + 1 37 2
8 8 8 = 6+ =
6 6 3
1 1 (iii) Find the fraction value of x+x× = 1320
= 400% + 37 % = 437 % 8
2 2 2 8 x  3x
366 % = 1320
33 3 8
(iii) Find the % value of
7 2 2 11x
366 % = 300% + 66 % = 1320
33 28 5 3 3 8
= +
7 7 7 2 11 8
=3+= x = 1320 × = 960
3 3 3 3 11
= 400 % + 71 % = 471 %
7 7 (iv) Find the fraction value of Fraction Method:
23 1 3 % result
(iv) Find the % value of 208 % 1
12 3 37 %=
2 8 Orignal Number
23 12 11 1 1 Original number = 8 unit
= + 208 % = 200% + 8 %
12 12 12 3 3 Result formed = 8 unit + 3 unit
2 2 1 25  1 
= 100% + 91 % = 191 %
3 3 =2+
12
=
12 8  37 2 %  3
 
Alternatively:
11 unit  1320
How to understand the actual
meaning of fraction. 1 unit  120
So, the original number = 8 ×
120 = 960
Percentage 2
 1 Original no. = 6 unit = 6 × 708 x = 36 × 4 = 144
2. If 62 % of a number is sub- = 4248 10. If 240 is 20% of a number, then
2
120% of that numbe will be ?
tracted from itself then result 2
4. If 6 % of a number is sub- sol. Let the number be = x
becomes 6321. Find the origi- 3 20% of x = 240
nal number. tracted from itself then result
becomes 5670. Find the origi- 1
Detailed Solution, x× = 240
nal number. 5
Let the original number = x
Sol. x = 1200
A.T.Q,
Now,
x – x × 62 1 % = 6321 2 1 Substract value
–6 % = 120
3 15 Original number 1200 × 120% = 1200 ×
2 100
New Value = 15 – 1 = 14 unit
5 = 1440
x– x× = 6321 = 5670
8 1 unit = 405 3
11. If we express 41 % as a
3x Original value = 405 × 16 17
= 6321 = 6480 fraction, then it is equal to :
8
x = 16856 1 3 700 1 7
5. If 11 % of a number is added Sol. 41 % = × =
Fraction method : 9 17 17 100 17
1 5 with itself then result 12. If 125% of x is 100, then x is:
62 %=
2 8 becomes 900 find the original 125
number. Sol. x × =100
 1  100
8  62 2 %  5  1
  1 Added value 100 ´ 100
Sol. + 11 % = 9 x= = 80
Original number = 8 unit 9 Original number
125
Result formed = 8 unit – 5 unit New value = 9 + 1 = 10 unit 13. If 50% of (x - y) = 30% of (x + y)
3 units  6321 = 900 then what percent is y of x ?
1 unit  2107 1 unit = 90
50 30
So, original number Original no. = 90 × 9 = 810 Sol. (x - y) = (x + y)
100 100
= 8 × 2107 = 16,856 6. What is 20% of 50% of 75%
50x – 50y = 30x + 30y
of 70?
2 50x – 30x = 30 y + 50 y
3. If 16 % of a number is added 1 1 3 20x = 80 y
3 Sol. Value = 70 × × ×
5 2 4 x =4
with itself then result
becomes 4956. Find the origi- 21 y=1
= =5.25
nal number. 4 1
7. If 20% of (P + Q) = 40% of So, y is = 25%
Sol. Let the original no. = x 4
According to the question (P – Q) then find P : Q 14. If 64 is added in a number then
2 20 40 1
x + x ×16 % = 4956 Sol. (P + Q) = (P – Q) number becomes 157 % of it-
3 100 100 7
P + Q = 2P – 2Q self. Find the number.
x P – Q = 4P – Q
x+ = 4956 1 11
6 3Q = 1P Sol. 157 %=
7 7
7x P:Q=3:1
= 4956  1 
6 8. What is 20% of 25% of 300 ?
7  157 7 %  11
x = 708 × 6 = 4248  
20 25
Alternate: Sol. 300 × × = 15 7 unit 11 unit
100 100
2 1 % result 9. 25% of what number is 36 ?
16 % =
3 6 Original number Sol. Let the number be x 4 unit  64
Now, 25 1 unit  16
New No = 6 + 1 = 7 unit = 4956 then x × = 36 So, the original number = 7 ×
100
1unit = 708 16 = 112

3 Percentage
15. If 930 is added in a number other is increased by 5%. Find
4
% change in Area = × 100 the percent value by which the
4 40
then number becomes 444 % area changes.
9 = 10% Sol. Area of rectangle = Length ×
of itself. Find the original num- 18. If the sides of a square is in- Breadth
ber. creased by 40%. Find the %
change in its area. 1
4 40 Length +20% =
Sol. 444 % = 5
9 9 Sol. Area
Side (Side)2 1
4 4 Breadth +5% =
444  400%  44 % 5 25 20
9 9 +24
4 40 L B Area
4  7 49
9 9 5 × 20 = 100
26
4  2 6 × 21 = 126
and 9 × 444 %  40
9 40%  5 
 
26
Required%=  100
Original number Formed number 24 100
9 unit 40 unit % change in Area = ×100 = 96%
25 = 26%  (Increase)
19. The price of sugar is increased
22. If one of the sides of rectangle
+ 31unit  930 2
by 16 % and; the consump- 1
1 unit  30 3 increased by 37 % and the
2
So, the original number = 9 × tion of a family is decreased by
30 = 270 other is decreased by 20% find
20%. Find the % change in his
the percent value by which area
16. The price of a commodity rise expenditure.
from ` 6 per kg to ` 7.50 per changes.
Sol.
kg. If the expenditure cannot in- Sol. Area = Length × Breadth
crease the percentage of reduc- Price Consumption Expenditure
6 × 5 = 30 1 3
tion in consumption is  2 1
16 3 %  6  –2 Length = 37 % 
2 8
Sol. Percentage increase 7 × 4 = 28
% change in his expenditure 1
7.50 - 6 Breadth = –20% 
= ×100 = 25% 5
6 2 2
= ×100 = 6 % L B Area
30 3
+25% 8 × 5 = 40
100 125 20. The sale of a cinema ticket is 4
11 × 4 = 44
–25 1
increased by 57 % and the 4
\ Percentage decrease in con- 7 Required % =  100 = 10% 
sumption price of ticket is increased by 40
(Increase)
25 2 23. A number is first reduced by
= ´ 100 = 20% 16 %. Find the % change in
125 3 20% and then it is increased
17. If the length of a rectangle is his revenue. by 80%. What was the net
Sol. Sale Price effect?
1 7 × 6 = 42
increased by 37 % and its +35
2
11 × 7 = 77 Sol. –20% = –1 , 5 4
breadth is decreased by 20%. 5
Find the % change in the area. 1 4 2 1 +4 , 5 9
57 %= , 16 %= +80% =
Sol. Length × Breadth = Area 7 7 3 6 5 25 36
8 × 5 = 40
% Change in his revenue +11
+4
11 × 4 = 44
35 1
 ×100  83 % 11
 1 3  1 42 3 Required % =  100
37 2 %  8  20%  5 
25
    21. If one of the sides of a rectangle
= 44% (Increase)
is increased by 20% and the
24. The tax imposed on an article

Percentage 4
 is increased by 10% and its Sol. Let the third number be = 100
1
consumption decreased by Required % =  100 I II III
10%. Find the percentage 100
120 150 100
change in revenue from it. = 1% (decrease)
25. Two numbers are respectively 120
1 , Then,  100 = 80%
Sol. I +10% = 10 11 20% and 50% more than a 150
10
third. Now what percentage is
1 10 9 the first of the second?
II –10% = 10 ,
100 99
–1

Exercise

1. Student A scores 20 marks in (c) 10% increase he donated 20% to a charity.

an examination out of 30 while (d) None of these Further he purchases a flat in
another student B scores 40 Ganga Apartment for Rs. 7.5
6. Due to a 25% price high in the
marks out of 70. Who has lakh. He then realises that he
price of rice, a person is able to
is left with only Rs. 2.5 lakh
performed better ? purchase 20 kg less of rice for
cash of his inheritance. What
(a) A (b) B Rs. 400. Find the initial price.
was the value of his inheritance
(c) A = B (a) 4 Rs/kg (b) 5 Rs/kg ?
(d) Can’t be determined (c) 8 Rs/kg (d) None of these (a) 25 lakh (b) 22.5 lakh
2. Company A increases its sales 7. A’s salary is 20% lower than B’s (c) 20 lakh (d) 18 lakh
by 1 crore rupees while com- salary, which is 15% lower than 10. What is 20% of 50% of 75% of
pany B increases its sales by C’s salary. By how much per- 70?
10 crore rupees. Which com- cent is C’s salary more than A’s
(a) 5.25 (b) 6.75
pany has more percentage salary?
(c) 7.25 (d) 5.5
growth? 1 1
(a) 47 % (b) 48 % 3
(a) A (b) B 7 7 11. If we express 41 % as a frac-
17
(c) Both have same growth rate 2 tion, then it is equal to
(d) Can’t be determined (c) 47 % (d) None of these
7 17 7
3. The population of a city grew 8. The cost of manufacture of an (a) (b)
7 17
from 20 lakh to 22 lakh. Find article is made up of four com-
the percentage change based on 12 3
ponents A, B, C and D which (c) (d)
the final value of population. have a ratio of 3 : 4 : 5 : 6 re- 17 17
spectively. If there are respec- 12. Mr. Rakesh Yadav is worried
1 about the balance of his
(a) 9 % (b) 8% tive changes in the cost of +10%,
11 –20%, –30%, and +40%, then monthly budget. The price of
(c) 9% (d) 10% what would be the percentage petrol has increased by 40%. By
4. A sells his goods 30% cheaper change in the cost. what percent should he reduce
than B and 30% dearer than C. the consumption of petrol so that
2 2
By what percentage is the cost (a) 2 % (b) 3 % he is able to balance his budget?
9 9 (a) 33.33 (b) 28.56
of C’s goods cheaper than B’s
goods. 2 (c) 25 (d) 14.28
(c) 4% (d) 1 % 13. In Question 12, if Rakesh Yadav
(a) 46.15% (b) 47.15% 9
(c) 67% (d) 67.15% wanted to limit the
9. Rakesh Yadav receives an inher-
itance of a certain amount from increase in his expenditure to
5. The length and the breadth of
his grandfather. Of this he 5% on his basic expenditure on
a rectangle are changed by +
loses 32.5% in his effort to pro- petrol, then what should be the
20% and by –10% respectively.
duce a film. From the balance, corresponding decrease in con-
What is the percentage change
a taxi driver stole the sum of sumption.
in the area of the rectangle.
Rs. 1,00,000 that he used to (a) 33.33 (b) 28.56
(a) 8% increase
keep in his pocket. Of the rest, (c) 25 (d) 20
(b) 8% decrease

5 Percentage
14. Ram sells his goods 25% (a) 1.5a (b) 0.667a population at the end of the
cheaper than Shyam and 25% (c) 0.5a (d) 1.25a third year if in the third year
dearer than Balram. How 21. The length, breadth and height the population increases by
much percentage is Balram’s of a room in the shape of a 20%.
goods cheaper than Shyam’s ? cuboid are increased by 10%, (a) 12,340 (b) 12,540
(a) 33.33% (b) 50% 20% and 50% respectively. Find
(c) 66.66% (d) 40% (c) 1,27,540 (d) 12,340
the percentage change in the
15. In an election between 2 candi- volume of the cuboid. 27. Rakesh Yadav inv ests Rs.
dates, Rakesh Yadav gets 65% 10,000 in some shares in the
(a) 77% (b) 75%
of the total valid votes. If the to- ratio 2 : 3 : 5 which pay
(c) 88% (d) 98%
tal votes were 6000, what is the dividends of 10%, 25% and 20%
number of valid votes that the 22. The price of sugar is reduced
(on his investment) for that year
other candidate Bhuvnesh gets, by 25% but inspite of the
respectively. Find his dividend
if 25% of the total votes were de- decrease, Aayush ends up
income.
clared invalid ? increasing his expenditure on
sugar by 20%. What is the (a) 1900 (b) 2000
(a) 1625 (b) 1575
(c) 1675 (d) 1525 percentage change in his (c) 2050 (d) 1950
monthly consumption of sugar ? 28. In an examination, Rakesh
16. In a medical certificate, by mis-
(a) +60% (b) –10% Yadav obtained 20% more than
take a candidate gave his height
as 25% more than normal. In (c) +33.33% (d) 50% Bhuvnesh but 10% less than
the interview pannel, he clari- 23. When 60% of number A is Pawan. If the marks obtained
fied that his height was 5 feet 5 added to another number B, B by Bhuvnesh is 1080. find the
inches. Find the percentage becomes 175% of its previous percentage marks obtained by
correction made by the candi- value. Then which of the Pawan if the full marks is 2000.
date from his stated height to following is true regarding the (a) 86.66% (b) 72%
his actual height. values of A and B ? (c) 78.33% (d) 77.77%
(a) 20% (b) 28.56% (a) A > B (b) B > A
(c) 25% (d) 16.66% 29. In a class, 25% of the students
(c) B  A were absent for an exam. 30%
17. Arjit Sharma generally wears
his father’s coat. Unfortu- (d) either (a) or (b) can true failed by 20 marks and 10% just
nately, his cousin Shaurya depending upon the values passed because of grace marks
poked him one day that he was of A and B of 5. Find the average score of
wearing a coat of length more 24. In an election, the candidate the class if the remaining
than his height by 15%. If the who got 56% of the votes cast students scored an average of
length of Arjit’s father’s coat is won by 144 votes. Find the total 60 marks and the pass marks
120 cm then what should be number of voters in the voting are 33 (conunting the final
the actual length of the his list if 80% people cast their vote scores of the candidates).
coat. and there were no invalid votes. (a) 37.266 (b) 37.6
(a) 105 (b) 108
(a) 360 (b) 720 (c) 37.8 (d) 36.93
(c) 104.34 (d) 102.72
(c) 1800 (d) 1500 30. Rakesh Yadav spends 20% of
18. A number is mistakenly divided his monthly income on his
25. The population of a village is
by 5 instead of being multiplied houshold expenditure, 15% of
by 5. Find the percentage 1,00,000. The rate of increase
is 10% per annum. Find the the rest on books, 30% of the
change in the result due to this
population at the start of the rest on clothes and saves the
mistake.
third year. rest. On counting, he comes
(a) 96% (b) 95% to know that he has finally
(c) 2400% (d) 200% (a) 1,33,100 (b) 1,21,000
saved Rs. 9520. Find his
19. The price of an item is increased (c) 1,18,800 (d) 1,20,000 monthly income.
by 20 % and then decreased by 26. The population of the (a) 10000 (b) 15000
20 % . The final price as Mukherjee Nagar is 10,000 at
(c) 20000 (d) 12000
compared to original price is: this moment. It increases by
10% in the first year. However, 31. Rakesh Yadav and Bhuvnesh
(a) 20 % less (b) 20 % more
have salaries that jointly
(c) 4 % more (d) 4 % less in the second year, due to
amount to Rs. 10,000 per
20. 50% of a% of b is equal to 75% of immigration, the population
month. They spend the same
b% of c. Which of the following is c? drops by 5%. Find the

Percentage 6
 amount monthly and then it is price of the cow and that of the said that it usually sold for 8/
found that the ratio of their calf is increased by 20% and 7 of that price. He then offered
savings is 6 : 1. Which of the 30% respectively then the price me the other shirt for Rs. 36
following can be Rakesh of 1 dozen cows and 2 dozen and said that it usually sold for
Yadav’s salary ? calves is: 7/6th of that price. Of the two
(a) Rs 6000 (b) Rs 5000 shirts which one do you think
(a) 72,480 (b) 71,360
(c) Rs 4000 (d) Rs 3000 is a better bargain and what is
(c) 74,340 (d) None of these
32. The population of a village is the percentage discount on it ?
37. During winters, an athlete can
5500. If the number of males
run ‘x’ meters on one bottle of (a) First shirt, 12.5%
increase by 11% and the number
of females increases by 20% then Glucose. But in the summer, (b) second shirt, 14.28%
the population becomes 6330. he can only run 0.5x meters on
(c) Both are same
Find the population of females one bottle of Glucose. How
many bottles of Glucose are (d) None of these
in the town.
(a) 2500 (b) 3000 required to run 400 meters 41. 4/5th of the voters in Delhi
(c) 2000 (d) 3500 during summer ? promised to vote for Rakesh
33. Bhuvnesh’s salary is 75% more (a) 800/x (b) 890/x Yadav and the rest promised to
than Saurabh’s. Bhuvnesh got (c) 96 (d) 454/x vote for Bhuvnesh. Of these
a raise of 40% on his salary voters, 10% of the voters who
38. Out of the total production of
while Saurabh got a raise of iron from hemetite, an ore of had promised to vote for
25% on his salary. By what Rakesh Yadav did not vote on
iron, 20% of the ore gets
percent is Bhuvnesh’s salary the election day, while 20% of
wast ed, and out of the
more than Saurabh’s ? the voters who had promised to
remaining ore, only 25% is pure
(a) 96% (b) 51.1% vote for Bhuvnesh did not vote
iron. If the pure iron obtained
(c) 90% (d) 52.1% on the election day. What is the
in a year from a mine of
34. Last year, the Indian cricket total number of votes polled if
hematite was 80,000 kg, then
team played 40 one day cricket
the quantity of hematite mined Rakesh Yadav got 216 votes ?
matches out of which they
managed to win only 40%. This from that mine in the year is (a) 200 (b) 300
year, so far it has played some (a) 5,00,000 kg (c) 264 (d) 100
matches, which has made it
(b) 4,00,000 kg 42. In an examination, 80%
mandatory for it to win 80% of
the remaining matches to (c) 4,50,000 kg students passed in Physics,
maintain its existing winning (d) None of these 70% in Chemistry while 15%
percentage. Find the number of failed in both the subjects. If
mathes played by India so far 39. A man buys a truck for Rs.
2,50,000. The annual repair 325 students passed in both
this year.
cost comes to 2.0% of the price the subjects. Find the total
(a) 30 (b) 25
of purchase. Besides, he has number of students who
(c) 28 apperared in the examination.
to pay an annual tax of Rs.
(d) Insufficient Information
2000. At what monthly rent (a) 500 (b) 400
35. In the recent, climate must he rent out the truck to (c) 300 (d) 600
conference in New York, out of get a return of 15% on his net
700 men, 500 women, 800 43. Rakesh Yadav spends 30% of
investment of the first year ? his salary on house rent, 30%
children present inside the
(a) Rs 3350 (b) Rs 2500 of the rest he spends on his
building premises, 20% of the
men, 40% of the women and (c) Rs 4000 (d) Rs 3212.50 children’s education and 24%
40. Recently, while shopping in of the total salary he spends on
10% of the children were
Mukherjee Nagar, Delhi, I came clothes. After his expenditure, he
Indians. Find the percentage
across two new shirts selling at is left with Rs. 2500. What is
of people who were not Indian.
a discount. I decided to buy Rakesh Yadav’s salary ?
(a) 73% (b) 77%
one of them for my little boy (a) Rs 11,494.25
(c) 79% (d) 83%
Sherry. The shopkeeper offered (b) Rs. 20,000
36. A cow and a calf cost Rs. 2000
me the first shirt for Rs. 42 and (c) Rs 10,000
and Rs. 1400 respectively. If the

7 Percentage
 (d) Rs.15,000 year, the share of Honda in that 49. At IIM Bangalore, 60% of the
44. The entrance ticket at the Batra year was: students are boys and the rest
cinema in Delhi is worth Rs. (a) 50% (b) 45% are girls. Further 15% of the boys
250. When the price of the (c) 40% (d) 60% and 7.5% of the girls are getting
ticket was lowered, the sale of 47. Ambani, a very clev er a fee waiver. if the number of
tickets increased by 50% while businessman, started off a those getting a fee waiver is 90,
the collection recorded a business with very little capital, find the total number of students
decrease of 17.5%. Find the In the first year, he earned a getting 50% concession if it is
deduction in the ticket price profit of 50% and donated 50% given that 50% of those not
(a) Rs 150 (b) Rs. 112.5 of the total capital (initial getting a fee waiver are eligible to
(c) Rs 105 (d) Rs. 120 capital + profit ) to a charitable get half fee concession?
45. Rakesh Yadav’s monthly salary organisation. The same course (a) 360 (b) 280
is A rupees. Of this , he spends was followed in the 2nd and 3rd
(c) 320 (d) 330
X rupees. The next month he years also. If at the end of three
years, he is left with Rs. 50. A machine depreciates in value
has an increase of C% in this each year at the rate of 10% of
salary and D% in his 16,875, then find the amount
donated by him at the end of its previous value. However,
expenditure. The new amount every second year there is some
saved is: the 2nd year.
maintenance work so that in
(a) A(1+C/100) – X (1+D/100) (a) Rs 45,000(b) Rs 12,500 t h a t
(b) (A/100) (C – (D) X (1+D/100) (c) Rs 22,500 (d) Rs 20,000 particular year, depreciation is
(c) X(C – (D)/100 48. In an examination, 48% only 5% of its previous value.
students failed in Hindi and If at the end of the fourth year,
(d) X(C + D)/100 the value of the machine stands
32% students in History, 20%
46. In the year 2000, the luxury car students failed in both the at Rs. 1,46,205, then find the
industry had two car subjects. If the number of value of machine at the start of
manufactures – Maruti and students who passed the the first year.
Honda with market shares of examination was 880, how (a) Rs 1,90,000
25% and 75% respectively. In many students appeared in the
2001, the overall market for the (b) Rs 2,00,000
examination if the examination
product increased by 50% and (c) Rs 1,95,000
consisted only of these two
a new player BMW also entered subjects ? (d) Rs 2,10,000
the market and captured 15%
(a) 2000 (b) 2200
of the market share. If we know
that the market share of Maruti (c) 2500 (d) 1800
increased to 50% in the second

Percentage 8
 Solution
1. (a) % Marks score by the student A 5. (a) Let
20 2 Length × Width = Area
= ×100 = 66 % Old 10 10 = 100
30 3
+20% –10%
% Marks score by the student B
New 12 9 = 108
40 1 Increased in Area = 108 – 100 = 8
= ×100 = 57 %
70 7
8
Now it is clear that the performance of A is better. % increased = ´ 100 = 8% Ans.
100
Alternatively  (a)
Alternatively 
Marks Score Out of Note:- In such type of questions we can use the
A 20×7 30 7 below given formula.
210
3  XY    Shows increase 
B 40×3 70  X + Y+ 100   – Shows decrease 
   
Note:- Equal the out of marks then we can directly
20  10
analyse the performance. Change in area = 20 – 10 – = 8%
100
Marks Score Out of
A  140 210 Sign is +ve so increase in area = 8%
B  120 210 6. (a) According to the question :-
Now we can say performance of A is better. Rise in the price = 25%
2. (d) Apparently, the answer to the question seems 25
to be company B. The question can not be an- % Reduction in consumption = ×100 = 20%
125
swered since we don’t know the previous year’s
sales figure. But actual reduction in consumption = 20kg
3. (d) Percentage change based on the final value  20% = 20 kg

2 100
20
= ×100 = % = 10% 1% = kg
20 10 20

4. (a) Let the price of B = Rs. 100 20

Now According to the question :- original consumption (100%) = ×100
20
A : B : C = 100 kg
700 Money spent = 400 Rs (Given)
70 : 100 :
13 400
Original price = = Rs 4/kg
Note:- Make the ratios in such a way that can not 100
generate fractions: Alternatively:- Let the expenditure = 100 Rs
 Multiply 13 in all ratios.
A : B : C 100
910 : 1300 : 700 +25
–25
The percentage by which C’s price is cheaper than
1300 – 700  125
B’s price= ×100
1300
5 1 4 New
 = =
600 125 5 5  Original
= = 46.15%
13 1 unit  20 kg

9 Percentage
 Original consumption = 20 × 5 = 100 kg Alternatively-
New consumption = 4 × 20 = 80 kg Note:- These type of problems should either be
solved through the reverse process or through op-
400 tions.
Original price of the rice = = Rs 4/kg
100 Option (c):- Total value of inheritance = 20 lakh
7. (a) Note :- In such type of question try to make According to the question:-
ratio between all the given variables.
–32.5%
20 lakh 13.5 Lakh –1 Lakh 12.5 Lakh

A : B B : C –20% =
1 2.5 Lakh –7.5 Lakh 10 Lakh –20%
5
Ratio of Salary 4 : 5 17 : 20 Same as mention in question.
3
15% = So option (c) is correct.
20
1 1 3 21
Combine the ratio of salary :- 10. (a) Value = 70    = = 5.25
5 2 4 4
A: B 4 : 5
3  697  3  1 700
11. (b) 41 %=   =
B: C 17 : 20 17  17  100 17  100
A : B : C
Ratio 68 : 85 : 100 7 
=  
17 
100 – 68 
C’s salary more than A = ×100 12. (b) Note  (1) If the price of a commodity in-
68
creases by r %, then the reduction in consump-
tion so as not to increase the expenditure is
32 8 800 1
= ×100 = ×100 = = 47 %
68 17 17 17  r 
=   100  %
8. (a) Note :- In such type of questions assume any  100  r  
value but ratio should not be changed.
(2) If the price of a commodity decreases by r%
A : B : C : D
then increase in consumption, so as not to
Old cost  300 : 400 : 500 : 600 decrease expenditure on this item is

+10% –20% –30% +40%  r 

=   100  %
 100 – r  
New cost  330 320 350 840
Use above these two methods to save your
Total old cost = (300+400+500+600) = 1800 Rs.
valuable time.
Total New cost = (330+320+350+840) = 1840 Rs.
40
1840 – 1800  40 2 % Reduction in consumption = 100  40 
% Change = ×100 = = 2 %
1800 18 9
9. (c) Let the inheritance value Recieved by Rakesh 40 400 200
=  100 = = = 28.57%
Yadav = x 140 14 7
According to the question:- 13. (c) Let the expenditure = 100 Rs.
After increase of 40% = 140 Rs.
 100 – 32.5  
x  – 100000  × 80 According to the question,
 100  100 Increase in expenditure should be only 5%= 105
= (750000 + 250000) 140 – 105 
% Reduction =  100
 67.5  80 140
 x  100 – 100000   100 = 1000000
 
x = 2000000, x = 20 Lakh

Percentage 10
 35 2
 100 = 25% c = a = 0.667a
% Reduction = 3
140
21. (d) Old New
14. (d) Ram : Shayam Ram : Bram Length 10 11
 1 3 : 4 5 : 4 Breadth 5 6
 25% =
 4  Height 2 3
Note :- The price of Ram’s goods should be equal Volume 100 198
in both cases. So equal the prices.
Ram : Shyam : Bram +98
15 : 20 : 12
98
% Bram’s goods cheaper than Shyam’s % Change in volume =  100 = 98%
100
 20 – 12 Alternatively : -
= ×100 = 40 %
20 Let initial volume = 100
15. (b) Let the total number of valid votes get by
Bhuvnesh = x 110 120 50
New volume = 100×  
According to the question:- 100 100 100

75 100–65 75 35 %change = 98%

x = 6000  = 6000   22. (a) Let the initial expenditure = 100
100 100 100 100
x = 1575 Initial Expenditure
100
%
16. (a) Note :- We can assume any value as the height –25
of the candidate to save your valuable time. +20%
New 75
Let height = 4x feet Expenditure
+45 120 Final expenditure
125
After increament = 4x × = 5x feet
100 120 – 75 
% reduction in height to get original value % change in consumption = ×100
75
 5 x – 4x 
=  100 = 20 % 45
5x =  100 = 60%
75
120 23. (d) According to the question :-
17. (c) Actual length of Arjit’s coat =  100
115 60% A + B = 175% B
= 104.34 cm
3 7
18. (a) Let the number = 5 A+B = B
5 4
According to the question:-
Case (I):- On dividing 3 3B
A =
5 5 4
New number (N1 ) = = 1
5
A B
Case (II):- On multiplication =
5 4
New number (N2) = 5×5 = 25
A : B = 5:4
 25 – 1
% change in result = ×100 = 96% Apparently it seems that A is bigger, but if you
25
consider A and B to be negative the opposite would
19. (d) Let original price = 100
be true.
 First new price = 120
Hence option (d) is correct.
& Final price = 80 % of 120 = 96
24. (d) Let the total number of votes = x
 Final price is 4 % less than the original price.
According to the question :-
1 a 3 b
20. (b) × ×b = × ×c 80 12
2 100 4 100 x× × = 144
a 3 100 100
3
= c  a = c
2 4 2

11 Percentage
 27. (d) Ratio of shares = 2x : 3x : 5x
144  100  100
x = = 1500 According to the question,
80  12
(2x + 3x + 5x) = 10,000
Total votes = 1500
10x = 10,000
Alternatively :-
x = 1000
(d) Let the cast votes = 100
Ist share = 2×1000 = 2000 Rs.
100 IInd share = 3×1000 = 3000 Rs.
Winner Loser IIIrd share = 5×1000 = 5000 Rs.
56 44 Divident income
12
2000  10 3000  25 5000  20
12 units = 144 = + +
100 100 100
1 unit = 12
= 200 + 750 + 1000 = 1950
Total cast votes = 12×100 = 1200
According to the question :- 1 1
28. (b) 20% = , 10% =
5 10
1200
Total number of votes =  100 = 1500 According to the question :-
80
Rakesh Yadav : Bhuvnesh Rakesh Yadav : Pawan
1
25. (b) 10% = Marks 6 : 5 9 : 10
10
Marks of Rakesh Yadav will be equal in both cases.
Old population New population Rakesh Yadav : Bhuvnesh : Pawan
Ist year 10 11
Ratio of marks:- 18 : 15 : 20
II Year
nd
10 11
100 121  × 72
According to the question:- 1080
100 units = 100,000 Marks obtained by Pawan = 20×72 = 1440
1 unit = 1000 1440
121 units = 121 × 1000 = 121,000 % marks =  100 = 72%
2000
Alternatively:-
29. (b) Passing marks = 33 [Given]
(b) Let the population at the start of the third
year = x Let the total number of Students = 100
According to the question:-
110 110
x = 100,000 × × 30   33 – 20   10  33  35  60
100 100 avg. =
100
x = 121,000
26. (b) The population of Mukherjee Nagar = 10,000 30  13  330  2100
avg. =
75
110 95 120
New population = 10,000× × × 390  330  2100
100 100 100 = = 37.6
75
= 12,540 30. (c) Let the monthly income of Rakesh Yadav = Rs x.
Alternatively :- (b) According to the question :-
Old New
80 85 70
(+10%) Ist year 10 11 x×   = 9520
100 100 100
(–5%) IInd year 20 19
x = 20,000
(20%) IIIrd year 5____ _6__
Monthly income of Rakesh Yadav = Rs. 20,000
1000 1254
31. (a) The only logic for this question is that Rakesh
According to the question :-
Yadav’s salary would be more than Bhuvnesh’ sal-
1000 units = 10000 ary. Thus, only option (a) is possible for Rakesh
1 unit = 10 Yadav’s salary.
Total New population = 1254×10 = 12540 32. (a) population of the village = 5500

Percentage 12
 After increament new population of the village = (700+500+800) = 2000
= 6330 Total people who were not Indian
 6330 – 5500  = 560 + 300+720 = 1580
% increment =  100
5500 1580
% people who were not Indian =  100 = 79%
2000
830 166
= = % 36. (a) 1 Cow: 1 Calf
55 11
Male% : Female% Old Cost  2000 : 1400
11% 20 %
+20% +30%

166 New Cost  2400 1820

%
11 According to the question :-
Price of 1 dozen cows = 2400×12 = 28800
Ratio of Male : Price of 2 dozen calves = 1820×24 = 43680
 166   166 
& Female  11 – 11  20 – 11  Total cost = 28800+43680 = Rs. 72,480
   
37. (a) According to the question :-
6 : 5 = 11 0.5x metres = 1 bottle
According to the question:-
11 units = 5500 1
1 metre = bottle
1 unit = 500 0.5x
Number of females = 500×5 = 2500
1 800
33. (a) Bhuvnesh : Saurabh 400 metres = ×400 = bottles
0.5x x
Ratio of salary = 700 : 400
38. (b) Let the total quantity of hematite mined =100 kg.
é 3ù According to the question:-
êë 75%= 4 ú
û
100 kg
Note :- Assume any value of salaries which can
not make fractions but remember one thing ratio –20% wasted
should not be changed.
According to the question:-
80 kg
Bhuvnesh : Saurabh re
pu Non
%
Old salary 700 : 400 25 iron pure
+40% +25%
kg 20 60 kg
New salary 980 500
+480  20 units = 80,000 kg
Percent of Bhuvnesh’s salary more than Saurabh’s 1 unit = 4,000 kg
480 480 Total hematite = 100 × 4000 = 4,00,000 kg
salary =  100 = = 96% 39. (d) The total cost of truck for a year =
500 5
34. (d) The data is in-sufficient since the number of 250,000  2
matches to be played by India this year is not 2,50,000 + + 2000 = Rs.257000
100
given. ( You can not assume that they will play 40
To get a return of 15% he must earn annualy
Matches).
35. (c) men : women : children 257000  15
= = Rs. 38550
700 : 500 : 800 100

38550
80% 60% 90% Hence, monthly rent = = Rs. 3212.50
12
Not Indian  560 300 720 40. (b) Note :- In such type of question no need to
Total people inside the premises calculate actual Market price and selling price. We
can simply calculate the ratio on the basis of given

13 Percentage
 fractions to save our valuable time.
325
According to the question:- 1% =
65
Condition (I) :- Let Market price = 8 Rs.
325
7 Total students (100%) = ×100 = 500
 Selling price = 8 × = 7 Rs 65
8
Total number of students appeared in the exami-
8 – 7 1 nation = 500
% Discount =  100 = 12 %
8 2 43. (c) Let the total salary of Rakesh Yadav =100 units
Condition (II) :- Similarly Salary spent on house rent
Selling price : Market Price 100  30
6 : 7 = = 30 units
100
1 2 Remaining salary = (100 – 30) = 70 units
% Discount = ×100 = 14 %
7 7 Salary spent on children’s education
Hence, the second shirt is a better bargain. 70  30
41. (c) Let the total number of voters = 500 = = 21 units
100
4 24
Voters who vote for Rakesh Yadav = 500× Salary spent on clothes = 100× = 24 units
5 100
= 400 Remaining salary = (100) – (30+21+24) = 25 units
Voters who vote for Bhuvnesh = (500 – 400) = 100 According to the question :-
Rakesh Yadav : Bhuvnesh 25 units = 2500 Rs
400 : 100
2500
1 unit = = 100 Rs
25
10% 20%
100 units = 100×100 = 10000 Rs.
[40] [20] Total salary of Rakesh Yadav = 10000 Rs.
Remaining Voters who voted = (500 – 60) = 440 Alternatively :-
Vote got by Rakesh Yadav = (400 – 40) = 360 Total salary
According to the question:- 100
24% Clothes
360 units = 216 Rem
30% aini
ng
Rent
216 70% 24
1 unit =
360 30 70
216
440 units = ×440 = 264 Education 30%
360
 Total votes polled = 264 21
42. (a)
Physics Chemistry Total spend money = 30+21+24 = 75
Remaining salary = (100 – 75) = 25
5% 15% 15% According to the question :-
25  2500
2500
[Failed venn diagram 1 
of students] 25
Total failed students = 5+15+15 = 35% 2500
 Total passed students = (100 – 35) = 65% Total salary = 100× = 10,000 Rs.
25
According to the question, 44. (b) Ticket price × no. of people = total collection
65% = 325

Percentage 14
 100 × 100 = 10000 Rs. According to the question:-
+50% –17.5% 150
x × 150 = 8250 Rs. New market share in 2001 = 100× = 150
100
8250 Total shares(2001)
x= = 55Rs.
150
150
% difference of ticket’s price Remaining
BMW
15% Maruti Honda
100 – 55
= ´ 100 = 45%
100 22.5 37.5 90

45
Now actual lowed price = 250× = 112.5 150
100 Maruti Shares = 25× = 37.5
100
Alternate:-
% share of Honda = = 60 %
According to the question :-
90
Final sales figure :-  100
150
50% 47. (c) Let the initial capital of the businesman = Rs.100
100
Sales increase 150
50
Collection 17.5% Profit = 100× = Rs.50
p 100
drop
dro
Total capital = (100 + 50) = Rs. 150
ice
Pr
82.5 50
Donation given = 150× = Rs. 75
100
150 – 82.5  67.5
Required price drop = = = 45% Remaining Capital after Donation = (150 – 75)
150 100
= Rs. 75
45 Initial Capital : Donation
Required value = 250× = Rs.112.5 100 : 75
100
45. (a) Rakesh Yadav’s monthly salary = A Rs. First year  4 : 3
Expenditure = X Rs. II year 
nd
4 : 3
IIIrd year  4 : 3
Note :- [ Savings = Income – expenditure ]
64 27
According to the question :-

A 100+C  ×625 ×625

New salary after increment =
100
[40,000] [16875]
New expenditure after increament
Capital for second year = 4 × 4 = 16
X 100+D  Donation for second year = 3 × 3 = 9
=
100  16 units = Rs.40,000
1 unit = 2500
A 100+C  X 100+D 
Savings = – Total donation = 2500×9 = Rs. 22500
100 100
Alternatively :-
 C   D 
Let the capital = x
= A 1+  – X 1+ 
 100   100 
46. (d) Let the total Market shares in 2000 = 100  150 50   150 50   150 50 
x        = 16,875
Total shares(2000)  100 100   100 100   100 100 
100 Ist year IInd year IIIrd year
Maruti Honda
+25% 75%

25 75

15 Percentage
 According to the question :-
 150 50   150 50 
x       = 22,500 (9 + 3) units = 90
 100 100   100 100 
90
Ist year IInd year 1 unit =
12
48. (b) Students failed in Hindi = 48% The number students who are not getting waiver
Students failed in History = 32% = (100 –12 ) = 88 units
Hindi English Total number of students getting 50% concession
90 1
28% 20% 12%
= 88 × ×  330
12 2
50. (b) Let the initial value of machine = x
According to the question,
(venn diagram of
failed students) 90 95 90 95
Number of students passed in the examination x× × × × = 146205
100 100 100 100
= (100 – 60) = 40% x = 2,00,000 Rs.
According to the question, Initial value of machine = Rs. 2,00,000
40 % = 880 Alternatively :- Old value New value
880 I year
st
 10 9
1% = IInd year  20 19
40
IIIrd year  10 9
880 IVth year  20 19
Total students = ×100 = 2200
40 40000 29241
49. (d) Let the total number of students = 100
Total students ×5 ×5
100
2,00,000 146205
Boys Girls Value of machine = Rs. 2,00,000

60 40
15% 7.5%
Getting Getting
Waiver 9 3
waiver

Percentage 16