Basic Concept of Percentage

It is a vital topic of arithmetic. It is a basic topic which used in various other topics as well like data interpretation, simplification, data sufficiency, etc. It is a very important topic and scoring for banking exams like IBPS, SBI. It covers 3 to 5 questions in IBPS Clerk preliminary exam and covers 6 to 8 questions in the main exam. 

Basic Concept of Percentage:- 

Percentage means per every hundred. Its base is 100. Its symbol is %.

Percentage Change:- Change in percentage can be calculated as:- (final value – initial value)×100/(initial value).

Successive Percentage Change:- Formula to find successive Percentage Change:- x + y – (x×y)/100, where x and y are percentage values.

When a value X is increased by b%, c%, and so on up to m% then the final result is:- 

⇒ X(1+b/100)(1+c/100)………..(1+m/100)

and if value X is decreased by b%, c% and so on up to m% then the final result is:-

⇒ X(1–b/100)(1–c/100)……..(1–m/100)

Some Important Percentage Values Asked In Exams Are Given Below:-

Percentage	Fraction
100%	1/1
10%	1/10
11.11%	1/9
9.09%	1/11
14.28%	1/7
15%	3/20
33.33%	1/3
7.14%	1/14
6 2/3%	1/15
8 1/3%	1/12
16 2/3%	1/6
25%	1/4
20%	1/5
37.5%	3/8
6.25%	1/16
7.69%	1/13

Some Questions Based On Percentage Are Given Below:

Q1. In a rectangle, length is increases by 33.33% and breadth is decreases by 37.5%. Find the Percentage Change in area.

a) increases by 16 2/3%. 
b) decreases by 16 2/3%. 
c) no change 
d) None of these
e) Can’t be determined

Solution:- 33.33% = 1/3, 37.5% = 3/8

Ratio of change in length:- 3 : 4

Ratio of change in breadth:- 8 : 5

Initial area:- 3×8 = 24 units

Final area:- 4×5 = 20 units

Percentage Change in area:- (24–20)×100/24 = 16 2/3%

Hence option b) is correct.

Q2. If a number 1300 is first decreases by 25% and then increases by 60%. Find the final number.

a) 1560 
b) 1450 
c) 1500 
d) none of these
e) Can’t be determined

Solution:- let the final number be x

1300 × 3/4 × 8/5 = x 

x = 1560 

Hence, option a) is correct.

Q3. Total population of a town is 10,50,000. The population of male is increased by 8% and population of females is increased by 5%. Overall increase in population is 6%. Find the ratio of male and female in the town.

a) 3:2 
b) 2:1 
c) 1:2 
d) 2:3 
e) None of these

Solution:- Let population of male and female is x and y respectively.

By using alligation, 

Male      :        Female 

8%                   5% 

             6% 

1            :          2 

On solving both equations, we get the ratio

x : y = 1:2

Hence, option c) is correct.

Q4. 35% of x is equal to 3.5 times of 20% of one-fifth of y. What percent of x is less than y?

a) 75% 
b) 60% 
c) 65% 
d) 40% 
e) none of these

Solution:- 35% × x = 3.5 × 20% × y/5 

(35×x)/100 = (35×2×y)/500 

x = 2y/5

x/y = 2/5

Required Percentage:- (5–2)×100/5 = 60%

Hence option b) is correct.

Q5. What percent of ₹125 is ₹50 ?

a) 30 
b) 35 
c) 40 
d) 45
e) None of these 

Solution:- (x × 125)/100 = 50 

x = 40

Hence option c) is correct. 

Q6. Kashyap scores 55% marks in a competitive exam. If he gets 363 marks,then find the maximum marks in the examination.

a) 600 
b) 630 
c) 660 
d) 560
e) None of these

Solution:- let maximum marks:- x 

x = 363×100/55

x = 660 

Hence option c) is correct. 

Q7. Suman saves 35% of her salary. If her expenditure is increased by 30% and her salary increased by 40%. Find the approximate increment in her savings. 

a) 58.57% 
b) 55.45% 
c) 59.35% 
d) 53.25%
e) None of these 

Solution:- let her salary is 100 

Income = savings + expenditure 

100 = 35 + 65 

Now, salary increased by 40% and expenditure increased by 30%. 

140 = new savings + 65×130/100(= 84.5) 

New savings:- (55.5–35)×100/35 

= 410/7 = 58.57% 

Hence option a) is correct. 

Q8. P is 55% of Q. Q is 40% of R. If P+Q+R = 162, find 2P+3Q-4R.

a) 118 
b) 85 
c) -85 
d) -236
e) None of these 

Solution:- 55% = 11/20 , 40% = 2/5 

P = 11/20 Q , Q = 2/5 R 

P:Q:R = 11:20:50 = 81 units

Value of 1 unit = 162/81 = 2 

P=22, Q=40, R=100 

= 2×22 + 3×40 – 4×100 = -236 

Hence option d) is correct. 

Q9. Population of a village increased by 20% and 24% in consecutive years and decreased by 30% in next year. Find overall increase or decrease in the population. 

a) decreased by 4.16% 
b) increased by 4.16% 
c) increased by 6% 
d) decreased by 6%
e) None of these 

Solution:- Let initial population is 100 

= 100 × 120/100 × 124/100 × 70/100 

= 104.16 

Overall increase in population is 4.16% 

Hence option b) is correct. 

Q10. Ayusha owns 33 1/3% of a property. If 50% of the property that she owns is ₹1,20,000. Find the value of 60% of the property. 

a) 2,40,000 
b) 3,00,000 
c) 43,20,000 
d) 6,00,000
e) None of these 

Solution:- Let total property is x 

33.33% = 1/3 , 50% = 1/2

x × 1/3 × 1/2 = 1,20,000 

x = 7,20,000 

60% of the property:- (60×7,20,000)/100 

= ₹432000

Hence option c) is correct. 

Q11. Due to fall in manpower, production in a factory decreases by 40%. By what percentage should the working hours be increased to restore the original production? 

a) 33.33% 
b) 66.66% 
c) 14.28% 
d) 28.56%
e) None of these 

Solution:- 40% = 40/100 = 2/5 

Original production:- 5 

After decrement:- 3 

Percentage to restore the original production:- (5-3)×100/3 

⇒200/3 = 66.66% 

Hence option b) is correct.