## Percentage Increase

To increase a quantity by a percentage find the percentage of the quantity and add it to the original quantity.

Example 1: Increase 320 by 20%.

Solution. 20% of 320 = $$\frac{ 20}{ 100}$$ x 320 = 64

Therefore,            Increased amount = Rs 320 + Rs 64 = Rs 384.

## Percentage Decrease

To decrease a quantity by a percentage, find the percentage of the quantity and subtract it from the original quantity.

Example 2: Decrease 120 by $$12\frac{1}{2}$$ %.

Solution. $$12\frac{1}{2}$$% of 120

= Rs $$\frac{ 12.5}{ 100}$$ of 120

= Rs $$\frac{ 125 }{ 10 * 100}$$ x 120

= Rs 15

Therefore,       Decreased amount = Rs 120 — Rs15 = Rs 105.

## Percentage Change

 Percentage change = ( $$\frac{ Actual change (Increase or Decrease)}{ Original quantity}$$ x 100) % Percentage error = ($$\frac{ Error}{Actual Value}$$ x 100) %

Example 3: Sabita’s weight decreased from 80 kg to 40 kg. Find the percentage decrease.

Solution. Decrease in weight = (80 — 40) kg = 40 kg.

Therefore,        % decrease = $$\frac{ 40}{ 80}$$ x100% = 50%.

Example 4: The distance between two places was 200 km. It was measured as 300 km. Find the percentage error.

Solution. Error = 300 km — 200 km = 100 km.

Therefore,     %error = $$\frac{ error}{ actual value}$$ x 100%

= $$\frac{ 100}{ 200}$$ x 100 = 50%.