# 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.

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