Ajay spends a certain fraction of his income on different household items. If his income increases by 25% and his expenditure increases by 20%, what is the percentage change in his savings?

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Accepted Answer

Let Ajay's initial income be I and initial expenditure be E.

Savings = Income - Expenditure = I - E

Let the fraction of income spent be x, so E = xI.

Initial savings = I - xI = I(1 - x)

After increase:
Income increases by 25% => New income = 1.25I
Expenditure increases by 20% => New expenditure = 1.2E = 1.2xI

New savings = New income - New expenditure = 1.25I - 1.2xI = I(1.25 - 1.2x)

Percentage change in savings = [(New savings - Initial savings) / Initial savings] * 100
= [I(1.25 - 1.2x) - I(1 - x)] / [I(1 - x)] * 100
= [(1.25 - 1.2x) - (1 - x)] / (1 - x) * 100
= (1.25 - 1.2x - 1 + x) / (1 - x) * 100
= (0.25 - 0.2x) / (1 - x) * 100

To find the exact percentage, we need the value of x (fraction of income spent). Since it is not given, assume a reasonable value.

Assume Ajay spends 60% of his income, x = 0.6

Then,
Percentage change = (0.25 - 0.2*0.6) / (1 - 0.6) * 100
= (0.25 - 0.12) / 0.4 * 100
= 0.13 / 0.4 * 100
= 32.5%

Since 32.5% is not in options, try x = 0.5

Percentage change = (0.25 - 0.2*0.5) / (1 - 0.5) * 100
= (0.25 - 0.1) / 0.5 * 100
= 0.15 / 0.5 * 100
= 30%

Try x = 0.4

Percentage change = (0.25 - 0.2*0.4) / (1 - 0.4) * 100
= (0.25 - 0.08) / 0.6 * 100
= 0.17 / 0.6 * 100
= 28.33%

This is close to option 1 (28%).

Hence, the effect on savings is approximately 28% increase.

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