Quant (Concepts): Percentage

Quant (Concepts): Percentage

Percentage Increase or Decrease of a Quantity

The increase or decrease is always on the original quantity. If the increase or decrease is given in absolute terms and percentage increase or decrease is to be calculated, then

The following formula is applied:

Percentage increase/decrease =

100 × (quantity increase / decrease) / original quantity

Example:

Salary of a man decreases from Rs. 100 to Rs. 75. What is the %age decrease in salary?

Solution:

Decrease = 100 – 75 = Rs. 25

% decrease = (25/100)×100 = 25%

To increase a number by x%

• If a number is increased by 10%, it becomes 1.1 times of itself.
• If a number is increased by 20%, it becomes 1.2 times of itself.
• If a number is increased by 30%, it becomes 1.3 times of itself, and so on.

To decrease a number by x%

• If a number is decreased by 10%, it becomes 0.9 times of itself
• If a number is decreased by 20%, it becomes 0.8 times of itself
• If a number is decreased by 30%, it becomes 0.7 times of itself, and so on.

Salary/Weight/Income Increase & Decrease

• If A’s income is R% more than that of B, the B’s income is less than that of A by 100 × [R/(100+R)] %.
• If A’s income is R% more than that of B, the B’s income is more than that of A by 100 × [R/(100-R)] %

Important results to remember:

If A is 16.67% less than B, then B is 20% more than A.

If A is 20% less than B, then B is 25% more than A.

If A is 25% less than B, then B is 33.33% more than A.

If A is 50% more than B, then B is 33.33% less than A.

Increase and Decrease by the same %

• If a number is increased by R%, then this number is decreased by R%, then in total there would be a decrease of (R²/100)%.