www.sakshieducation.

com

PERCENTAGE
Important Formulas:
1. If any number is divided by 100 then it is called a percentage. It is denoted by %.
x
⇒ x% =
100
∴ To get the fractional or decimal equivalent to a percentage divide the given number

m
with 100.

o
2. If a number is increased by x% then the value after increase is given by

.c
New Value (N.V.) = (100+x)% × Original Value (O.V.)
3. If a number is successfully increased by x%, y% and z% respectively, then the final value

n
is given by

io
Final Value (F.V.) = (100 + x)% × (100 + y)% × (100 + z)% × Initial Value (I.V.)
4. If a number is decreased or reduced by x% the value after reduction is given by

at
New Value (N.V.) = (100 – x)% × Original Value (O.V.)
5.
c
If a number is successively decreased by x%, y% and z% respectively then the final
du
value (F.V.) is given by
Final Value (F.V.) = (100 – x)% × (100 – y)% × (100 – z)% × Initial Value (I.V.)
6. If there are two different values (one is greater and the other is smaller) then the greater
ie

value is more than the smaller one in terms of percentage is given by

sh

Differenceof twovalues
%More = × 100
SmallerValue
ak

7. In the above case the smaller one less than the greater one in terms of the percentage is
given by
.s

Differenceof twovalues
% Less = × 100
GreaterValue
w

PROBLEMS
w

1. The price of sugar is increased by 25%. If a family wants to keep its expenses on
sugar unaltered, then the family will have to reduce the consumption of sugar by:
w

1) 20% 2) 21% 3) 22% 4) 25%

Ans: 1
Initial price be ’ 100 and consumption be 100 kg
∴ Total expense = 100 × 100 = 10,000
New price = 100 + 25 = 125
www.sakshieducation.com
 www.sakshieducation.com

But new expenditure = 10,000

10,000
∴ New consumption = = 80
125
So consumption of sugar reduced by 100 - 80 = 20%
2. Fresh grapes contain 80% water by weight, where as dried grapes contain 15%

m
water by weight. How many kg of dried grapes can be obtained from 3.4 kg of fresh
grapes?

o
1) 0.51 2) 0.6 3) 0.68 4) 0.8

.c
Ans: 4
20% of fresh grapes weight = 85% of dried grapes weight = 20% × 3.4 = 85% × ?

n
20 × 3.4 68 4

io
∴? = = = = 0.8
85 85 5

at
3. The population of a town 2 years ago was 2,45,000. It increased by 12% in the 1st
year and then increased by 15% in the second year. What is the current population
c
of the town?
du
1) 3,15,560 2) 2,74,400 3) 3,51,560 4) 2,94,560
Ans: 1
ie

New Value = (100 + 12)% × (100 + 15)% × 245000

112 115
sh

= × × 245000
100 100
112 × 115 × 245 3155600
ak

= =
10 10
= 3,15,560
.s

4. A number is first increased by 10% and then it is further increased by 20%. The
w

original number is increased altogether by?

1) 30% 2) 15% 3) 32% 4) 36%
w

Ans: 3
w

Let the number be 100.

Initially increased by 10%, the number becomes 110.
Then increasing by 20%, the number becomes 132.
∴ The original number is altogether increased by 32%.

www.sakshieducation.com
 www.sakshieducation.com

5. Ajay spends 25 percent of his salary on house rent, 5 percent on food, 15 percent on
travel, 10 percent on clothes and the remaining amount of ’ 27,000 is saved. What is
Ajay's income?
1) ’ 60,000 2) ’ 80,500 3) ’ 60,700 4) ’ 70,500
Ans: 1

m
Ajay's total income be 100%
His total expenditure = 25% + 5% + 15% + 10% = 55%

o
⇒ Savings = 100% – 55% = 45%

.c
∴ 45% → 27,000
27000 × 100

n
100% → ? = = 60,000
45

io
6. If the numerator of a fraction is increased by 200% and the denominator of the

at
9
fraction is increased by 120%, the resultant fraction is . What is the original
11
fraction?
c
du
2 4 1 3
1) 2) 3) 4)
5 5 5 5
Ans: 4
ie

p
Let be the original fraction.
sh

q
If numerator is increased by 200% then its value = (100 + 200)%× p = 300% p
If denominator is increased by 120% then its value = (100 + 120)%× q = 220% q
ak

300% p 9
∴ =
220% q 11
.s

p 9 220 9 3
⇒ = × = =
w

q 11 300 15 5
w

7. In a test Dilip scored 1269 marks and failed by 331 marks. Prakash scored 1723
w

marks which are 277 less than the maximum marks of the test. What is the minimum
passing percentage?
1) 90 2) 70 3) 60 4) None of these
Ans: 4
Minimum pass marks = 1269 + 331 = 1600

www.sakshieducation.com
 www.sakshieducation.com

Maximum marks = 1723 + 277 = 2000

1600
∴ Minimum pass percentage = × 100 = 80
2000
8. Anil scored 189 marks in Science, 156 marks in Hindi and 72 marks in Mathematics.
The maximum marks of Science are 210, Hindi are 180 and Mathematics are 110.

m
What percent of marks did Anil score overall?
1) 82.8 2) 82.6 3) 84.4 4) None of these

o
Ans: 4

.c
Total marks obtained by Anil in all subjects = 189 + 156 + 72 = 417
Total maximum marks in all subjects = 210 + 180 + 110 = 500

n
io
417
∴ Percentage of marks scored by Anil = × 100 = 83.4
500

at
9. 8% of the voters in an election did not cast their votes. In this election, there were
c
only two candidates. The winner by obtaining 48% of the total votes defeated his
du
contestant by 1100 votes. The total number of voters in the election was?
1) 21000 2) 23500 3) 22000 4) 27500
Ans: 4
ie

Total votes casted = 100–8 = 92%

sh

Out of 92%, one candidate gets 48%. So the other candidate gets 44%
Majority = 48% – 44% = 4% =1100
ak

Total number of voters = 100%

1100
= × 100 = 275 × 100 = 27500
4
.s

10. If 60% of A's income is equal to 75% of B's income, then B's income is equal to x%
w

of A's income. The value of x is?

w

1) 70 2) 60 3) 80 4) 90
Ans: 3
w

60% A = 75% B
60 75
⇒ ×A= ×B
100 100
⇒ 4A = 5B

www.sakshieducation.com
 www.sakshieducation.com

4A
∴B = × 100 = 80% A
5
∴ x = 80

11. The difference between 78% of a number and 56% of the same number is 429. What
is 66% of that number?

m
1) 1267 2) 1326 3) 1248 4) None of these

o
Ans: 4
Difference = 78% – 56% = 22% → 429

.c
429 3
∴ 66% of the number = × 66 = 1287

n
22

io
12. In an examination it is required to get 875 out of the aggregate marks to pass. A
student gets 630 marks and is declared failed by 14% marks. What are the

at
maximum aggregate marks a student can get?
1) 1750 2) 1775 3) 1825
c4) 1850
du
Ans: 1
Marks by which the student failed = 875 – 630 = 245 → 14%
ie

245
Maximum aggregate marks = 100% = × 100 = 17.5 × 100 = 1750
14
sh

13. 25 litres of salt solution contains 6% salt. How many litres of water must be added
so as to get a resultant solution containing 5% salt?
ak

1) 4 litres 2) 5 litres 3) 6 litres 4) 8 litres

Ans: 2
6
× 25 = 1.5
.s

Salt in 25 liters of salt solution =

100
w

Let x be the water added to the solution

Amount of water after addition = 1.5 + x
w

Amount of solution = 25 + x
w

1.5
∴ = 5%
25 + x
1.5 × 100 = 5 (25 + x)
150 = 125 + 5x
5x = 150 – 125 = 25

www.sakshieducation.com
 www.sakshieducation.com

25
∴x = =5
5

∴ The water to be obtained to the solution = 5 litres

14. In an examination in which full marks were 500, A got 10% less than B. B got 25%
more than C. C got 20% less than D. If A got 360 marks, what percentage of full

m
marks was obtained by D?

o
1) 90% 2) 80% 3) 50% 4) 60%

.c
Ans: 2
A's marks = 360

n
100
∴ B's marks = 360 × = 400

io
90
100

at
C's marks = 400 × = 320
125

D's marks = 320 ×

100
= 400
c
80
du

400
∴ D's percentage = × 100 = 80%
500
ie

10. 75 gm of sugar solution has 30% sugar in it. Then the quantity of sugar that should
sh

be added to the solution to make the quantity of the sugar 70% in the solution, is?
1) 125 gms 2) 100 gms 3) 120 gms
ak

4) 130 gms 5) None of these

Ans: 2
.s

75 × 30
Weight of sugar in the initial solution = = 22.5
100
w

If x grams of sugar is added to the initial

solution, then
w

22.5 + x = 70% (75 + x)

w

70
22.5 + x = (75 + x )
10 0
225 + 10x = 525 + 7x
3x = 525 – 225 = 300
∴ x = 100

www.sakshieducation.com
 www.sakshieducation.com

13. Sheela spends 18% of her monthly income for the children's education. She spends
32% of her monthly income in household expenses and 12% in travelling. She
spends 45% of the remaining amount in gambling and manages to save only ’ 9,405
at the end of the month. What is Sheela's monthly income?
1) ’ 36,000 2) ’ 50,000 3) ’ 45,000

m
4) Cannot be determined 5) None of these
Ans: 3

o
Let the total expenses be x

.c
Expenses on education, household expenses and travelling = (18 + 32 + 12)% of x
= 62% of x

n
Amount spent on gambling = 45% of (100–62) = 45% of 38% of x

io
Savings = 55% of 38% of x = 9,405

at
100 100
∴ x = 9405 × × = 45,000
38 55 c
14. In a test, minimum passing percentage for girls and boys are 45% and 60%
du
respectively. A boy scored 767 marks and failed by 313 marks. What are the
minimum passing marks for girls?
ie

1) 910 2) 920 3) 840 4) 810 5) None of these

Ans: 4
sh

Passing marks for boys = 767 + 313 = 1080

60% → 1080
ak

∴ 45% → ?
108 0
?= × 45 = 18 × 45 = 810
.s

60
∴ Passing marks for girls = 810
w
w

15. The sum of 18% of a number and 6% of the same number is 492. What is 12% of
that number?
w

1) 234 2) 242 3) 256 4) 264 5) None of these

Ans: 5
Sum of 18% and 6% = 18% + 6% = 24%
24% → 492

www.sakshieducation.com
 www.sakshieducation.com

492 × 12%
12% → ? = = 246
24%

Exercise
1. Three candidates contested an election and received 1136, 7636 and 11628 votes
respectively. What percentage of the total votes did the winning candidate get?

m
1) 57% 2) 60% 3) 65% 4) 90%

o
.c
2. In an examination it is required to get 65% of the aggregate marks to pass. A student
gets 522 marks and is declared failed by 7% marks. What are the maximum

n
aggregate marks a student can get?

io
1) 850 2) 780 3) 900 4) None of these

at
3. In a test, minimum passing percentage for girls and boys is 30% and 45%
c
respectively. A boy scored 280 marks and failed by 80 marks. How many more marks
du
did a girl require to pass in the test if she scored 108 marks?
1) 132 2) 140 3) 160 4) 112
ie

4. When the price of eggs is reduced by 20%, it enables a man to buy 20 more eggs for
sh

’ 40. The reduced price per egg is:

1) 35 paise 2) 40 paise 3) 50 paise 4) 56 paise
ak

5) Sanjay buys toys for Rs.7500. He gets a discount of 5% on it. After getting the
.s

rebate he pays sales tax at 10%. Find the amount he will have to pay for the toys?
1) 7800 2) 7500 3) 7600 4) 7837.50
w
w

Answers
w

1) 1 2) 3 3) 3 4) 2 5) 4

www.sakshieducation.com