What is “* PERCENTAGE*“?

It is a way of expressing a number as a fraction of 100. It is often denoted using the percent sign %.

For example, 56% = 56/100

#### Basic Concepts

Percentage Increase = ((Final value – Initial value)/(Initial value))*100

* Exercise 1*: The cost of a laptop was Rs. 25000 last year and due to inflation it increased to Rs. 30000. Find the percentage increase?

**Answer:**

Percentage Increase = ((F.V-I.V)/(I.V))*100 = ((30000-25000)/25000)*100 = 20%

Important point: If there is an increase in percentage on a quantity or number, the final value can be calculated by first converting % increase to decimal,* add 1* to it and multiply with the quantity.

Percentage Decrease = ((Initial value – Final value)/(Initial value))*100

**Exercise 2**: Manju weighted 80kg. Due to fever her weight is now 76kg. What is the percentage decrease in her weight?

**Solution**:

Percentage Decrease = ((I.V-F.V)/(I.V))*100 = ((80-76)/80)*100 = 5%

Important point: If there is an decrease in percentage on a quantity or number, the final value can be calculated by first converting percentage increase to decimal,* subtract it from 1* and multiply with the quantity.

### Shortcut Methods:

A. If a number A is P% more than B, then the value of B is (P/(100+P))*100 % less than A

**Example 3:** Manju scored 30% more than Vishal in a cricket match, then by what percentage is Vishal’s score less than Manju’s?

Solution:

Vishal percentage score is less than Manju by (p/(100+p))*100 % i.e., (30/(100+30))*100 = 23.076%

B. If the price of goods increases by P%, then the percentage reduction in consumption of goods, so that the final price remains the same is (P/(100+P))*100%

**Example 4**: If the price of sugar increases by 15% then by what % its consumption can be reduced so as to have the same expenditure?

Solution:

% decrease in sugar consumption = (15/(100+15))*100 = 13.04%

C. If number A is P% less than B, then the value of B is (P/(100-P))*100 % more than A

**Example 5**: If Vishal Salary is 25% less than Punit, then by what % is Punit salary more than Vishal?

Solution:

(25/(100-25))*100 = 33.33% higher

D. If the price of goods decreases by P%, then the percentage reduction in consumption of goods, so that the final price remains the same is (P/(100-P))*100%

**Example 6:** If the price of onion decreases by 20% then by what % its consumption can be increased so as to have the same expenditure?

Solution:

(20/(100-20))*100 % = 25%

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