On this page you will read information about important chapters of Mathematics, Percentage.

We have shared information about **Compound Interest** on the previous page, please read it.

Let us read and understand the information on the definition of percentage on this page.

## What is Percentage Called

The literal meaning of Percentage is per hundredth or hundredth or hundredth.

In other words, “Percentage is a Fraction whose denominator is 100 and the numerator of the fraction is called the rate of percentage, it is often represented by the % symbol.”

**Example :-** 10% means 10 out of 100. If a person spends 75% of his income, it means that he spends 75 out of 100 rupees.

If another person’s income is Rs 500 and he also spends 75%, then he spends 75% of Rs 500 i.e. Rs 375. This does not mean that he spends only Rs 75.

“Percentage is made up of two words per and shat which means ‘7% in every hundred’ means 7 in every hundred i.e. 7/100.

Therefore, this fraction whose denominator is 100 is called percentage and the numerator of the fraction is called the percentage rate.

It is often displayed by %, it has no units like Rs, meter, kilogram, liter etc.

## Percentage Formula

- Area of rectangle = length × breadth
- Area of square = side × side
- Volume of cube = side × side × side
- Volume of cuboid = length × width × height
- Volume of cylinder = πr²h
- Volume of cone = 1/3 πr²h
- Volume of sphere = 4/3 πr³

**Converting Percentages into Fractions**

35% | 35 | 7/20 |

48% | 48 | 12/25 |

72% | 72 | 18/25 |

6.40% | 64 | 4/250 |

80% | 80 | 4/5 |

**Converting Fractions into Percentages**

14/5 | 4/5 × 100 | 80% |

2/3 | 2/3 × 100 | 22/3% |

7/10 | 7/10 × 100 | 70% |

2/5 | 2/5 × 100 | 40% |

7/4 | 7/4 × 100 | 175% |

**Converting Percentage to Decimal**

18% | 18/100 | 0.18 |

274% | 274/100 | 2.74 |

47.60% | 47.6 | 0.476 |

71% | 71/100 | 1% |

**Convert Decimal to Percentage**

0.18 | 18/100×100 | 18% |

1.128 | 1128/1000×100 | 112.8 |

## Percentage Questions

Q.1 If Ram’s salary is 10% more than Anjali’s salary, then by what percent will Anjali’s salary be less than Ram’s salary?

A. 100/11

B. 200/3

C. 51/7

D. 97/9

Solution : According to the question,

Percentage increase/decrease = (% / 100+%) × 100

= 10 / 110 × 100

= 100/11

Ans. 100/11

Q.2 If A’s income is 25% more than B’s income, then by what percent is B’s income less than A’s income?

A. 100%

B. 20%

C. 60%

D. 40%

Solution : According to the question,

Percentage increase/decrease = (% / 100+%) × 100

= × 100

= 10 / 110 × 100

= 100/11

Ans. 100/11

Ans. 20%

Q.3 By increasing the numerator of a fraction by 10% and decreasing its denominator by 10%, the new fraction is 2/5, then tell the original fraction or the old fraction?

A. 7/11

B. 12/23

C. 18/55

D. 29/7

Solution : According to the question,

(100 + 10) / (100 – 10) = 2/5

110/90 = 2/5

2/5 × 9/11 = 18/55

Ans. 18/55

Q.4 If the price of rice decreases by 10%, a moneylender will lose Rs. 450. I buy 5 kg more rice, tell me what will be its new price and old price?

A. 4

B. 7

C. 9

D. 11

Solution : According to the question,

New price = % / 100 × Rs / item

= 10/100 × 450/5

= 9

Ans. 9 rupees per kilogram

Q.5 Due to increase in the price of pressure cooker by 20%, its sales decrease by 50%, how much percent less or more income will a shopkeeper get than before?

A. 10

B. 40

C. 30

D. 20

Solution : According to the question,

(100 +_ %) × (100 +_%) /100,

= (100% – reduction)

(100 + 20) × (100 – 50) / 100

= (120 × 50) / 100

= 60

= 100 – 60

Ans. There will be a reduction of 40%.

Q.6 If there is a 25% reduction in the price of a fan, its sales increase by 40%. Tell by what percentage will the income of a shopkeeper increase or decrease?

A. 5%

B. 8%

C. 2%

D. 6%

Solution : According to the Question,

(100 – 25) × (100 + 40) / 100

= (75 × 140) / 100

= 35 × 3

= 105

= (100 – 105)

Q.7 If Ram’s salary is 10% more than Anjali’s salary, then by what percent will Anjali’s salary be less than Ram’s salary?

A. 100/11

B. 200/3

C. 51/7

D. 97/9

Solution : According to the question,

Percentage increase/decrease = (% / 100+%) × 100

= 10 / 110 × 100

= 100/11

Ans. 100/11

Q.8 If A’s income is 25% more than B’s income, then by what percent is B’s income less than A’s income?

A. 10%

B. 20%

C. 25%

D. 40%

Solution : According to the question,

Percentage increase/decrease = (% / 100+%) × 100

= × 100

= 10 / 110 × 100

= 100/11

Ans. 100/11

Ans. 20%

Q.9 By increasing the numerator of a fraction by 10% and decreasing its denominator by 10%, the new fraction is 2/5, then tell the original fraction or the old fraction?

A. 7/11

B. 12/23

C. 18/55

D. 29/7

Solution : According to the question,

(100 + 10) / (100 – 10) = 2/5

110/90 = 2/5

2/5 × 9/11 = 18/55

Ans. 18/55

Q.10 If the price of rice decreases by 10%, a moneylender will lose Rs. 450. I buy 5 kg more rice, tell me what will be its new price and old price?

A. 4

B. 7

C. 9

D. 11

Solution : According to the question,

New price = % / 100 × Rs / item

= 10/100 × 450/5

= 9

### FAQ

**Q.1 What do you mean by percentage?**

**Ans. **In maths, a percentage is a value or ratio that shows a fraction of 100. Percent means per 100. It does not have any units.

**Q.2 What is the symbol of percentage?**

**Ans.** Percentage is denoted by ‘%’ symbol. It is also termed as per cent.

**Q.3 What is the percentage formula?**

**Ans.** The formula to calculate the percentage of a number out of another number is :

Percentage = (Original number/Another number) x 100

**Q.4 What is the percentage of 45 out of 150?**

**Ans.** (45/150) × 100 = 30%

**Q.5 What is 40% of 120?**

**Ans. **40% of 120

= (40/100) × 120

= 48

**Q.6 What is 20% out of 45?**

**Ans.** Multiply 20 by 45 and divide both sides by 100. Hence, 20% of 45 is **9**.

Hope you will like the information about percentage and you will be able to learn to calculate percentage after reading it.

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AnjuSuch a great insights and useful information in your blog

Easy Math Solutionthank you