The monthly income of a person was Rs. 13500/- and his monthly expenditure was Rs. 9000/-. Next year, his income increased by 14%…

Question

The monthly income of a person was Rs. 13500/- and his monthly expenditure was Rs. 9000/-. Next year, his income increased by 14% and his expenditure by 7%. Find the percentage increase in his savings.

1. A. 38%
2. B. 28% (Correct answer)
3. C. 32%
4. D. 45%

Correct Answer

Option B — 28%

Detailed Solution & Explanation

The correct answer is 28%.

Key Points

• Original savings = 13500 − 9000 = Rs. 4500.
• New income = 13500 × 1.14 = Rs. 15390.
• New expenditure = 9000 × 1.07 = Rs. 9630.
• New savings = 15390 − 9630 = Rs. 5760.
• Increase = 5760 − 4500 = 1260, so percentage increase = (1260 ÷ 4500) × 100 = 28%.

Additional Information

• Savings are a residual, so their percentage change is generally much larger than the change in either income or expenditure — here a 14% income rise against a 7% expenditure rise produces a 28% jump in savings.
• The general form is: new savings = I(1 + i) − E(1 + e), where I and E are the original income and expenditure and i, e their rates of change.
• This amplification is why questions of this type are set: candidates who average the two percentages, or apply them to the savings figure directly, arrive at a wrong answer that is usually one of the options.