The ratio of savings to expenditure of a woman is 2 ∶ 1. If her income and expenditure increase by 17% and 13% respectively, find the percentage increase in her savings.

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CRPF Constable Technical Tradesman Official Paper (Held On: 01 July, 2023 Shift 2)
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  1. 26%
  2. 28%
  3. 27%
  4. 19%

Answer (Detailed Solution Below)

Option 4 : 19%
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Detailed Solution

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Given:

The ratio of savings to expenditure of a woman is 2 ∶ 1.

Income increase = 17%

Expenditure increase = 13%

Formula Used:

Savings = Income - Expenditure

Calculations:

Let the original savings be 2x and the original expenditure be x.

Therefore, the original income = savings + expenditure = 2x + x = 3x.

New income = 3x × 1.17 = 3.51x

New expenditure = x × 1.13 = 1.13x

New savings = New income - New expenditure = 3.51x - 1.13x = 2.38x

Percentage increase in savings = (New savings - Original savings) / Original savings × 100

Percentage increase in savings = (2.38x - 2x) / 2x × 100 = 0.38x / 2x × 100 = 19%

∴ The percentage increase in her savings is 19%.

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