A man spends 75% of his income. Then his income rises by 20% and he increases his expenditure by 10% (relative to the old expenditure). By what percent do his savings increase?

Introduction / Context: Savings = Income − Expenditure. When both income and expenditure change by different percentages, compute new income and new expenditure carefully (noting the base of each change), then compare savings before and after.

Given Data / Assumptions:

• Initial income = I.
• Initial expenditure = 75% of I ⇒ 0.75I.
• Initial savings = I − 0.75I = 0.25I.
• New income = 1.20I (20% rise).
• New expenditure = 1.10 × (old expenditure) = 1.10 × 0.75I = 0.825I.

Concept / Approach: Compute new savings and then the percentage increase relative to the old savings. Be careful: the 10% increase applies to the old expenditure, not to the new income.

Step-by-Step Solution:

Verification / Alternative check: Let I = ₹100: initial savings ₹25. New income ₹120; new expenditure 1.10 × 75 = ₹82.5; new savings ₹37.5. Increase ₹12.5 on ₹25 = 50%.

Why Other Options Are Wrong: 25% and 37 1/2% mis-handle the base or apply 10% to the wrong quantity; 10% is far too small.

Common Pitfalls: Applying the 10% increase to the new income rather than the initial expenditure, or double-counting the 20% income rise as extra savings without adjusting expenditure.

Final Answer: 50%