A woman saves 18% of her income. If her income increases by 15% and her…

Concept

Savings = Income − Expenditure, so a change in savings depends on how income and expenditure move together. Any ‘percent decrease’ is found as (decrease ÷ the ORIGINAL value) × 100, using the original savings as the base — never the new income, new expenditure, or new savings. When a problem gives only percentages (no rupee figures), assume a convenient base income, such as 100, to convert the percentages into workable numbers.

Application

1. Let the initial income = 100. Since she saves 18% of her income, original savings = 18% of 100 = 18, and original expenditure = 100 − 18 = 82.

2. Income rises by 15%, so new income = 100 × 1.15 = 115.

3. Expenditure rises by 21.6%, so new expenditure = 82 × 1.216 = 99.712.

4. New savings = new income − new expenditure = 115 − 99.712 = 15.288.

5. Decrease in savings = original savings − new savings = 18 − 15.288 = 2.712.

6. Percent decrease in savings = (decrease ÷ original savings) × 100 = (2.712 ÷ 18) × 100 ≈ 15.1%.

Cross-check

Cross-check with a different base to confirm the percentage does not depend on the assumed income: with income = 1000, original savings = 180, new income = 1150, new expenditure = 820 × 1.216 = 997.12, new savings = 152.88, decrease = 27.12, and (27.12 ÷ 180) × 100 ≈ 15.1% — the same result, matching 15.1.