A girl spends 82% of her income. If her income increases by 15% and the…

Concept

When income is split between expenditure and savings, use the identity Income = Expenditure + Savings. A percentage change in one component should first be converted to an amount on a common base before comparing the final expenditure with the original expenditure.

Application

1. Let the original income be 100. Since 82% is spent, the original expenditure is 82 and the original saving is 18.

2. The new income is 100 x 1.15 = 115.

3. The saving decreases by 15%, so the new saving is 18 x 0.85 = 15.3.

4. The new expenditure is 115 - 15.3 = 99.7.

5. The increase in expenditure is 99.7 - 82 = 17.7.

6. The percentage increase is (17.7 / 82) x 100 = 21.585...%, which rounds to 21.6% to one decimal place.

Cross-check

On the original-income base, the saving changes from 18 to 15.3 while income changes to 115. Therefore expenditure changes from 82 to 99.7, giving the same percentage increase.

Result

The required percentage increase in expenditure is 21.6%.