## 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%.

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