The ratio of expenditure to savings of a woman is 4 : 1. If her income and expenditure are increased by 20% and 10%, respectively, then find the percentage change in her savings.

Correct — C. Treat the ratio parts as money, so both percentage rises land on whole numbers.

Expenditure : savings = 4 : 1, so income = 4 + 1 = 5
Income up 20%: 5 × 1.2 = 6
Expenditure up 10%: 4 × 1.1 = 4.4

New savings = 6 − 4.4 = 1.6
Change = (1.6 − 1) ⁄ 1 × 100 = 60% → option (c)

Why the others are wrong

• (a)
  50% — 50% would need new savings of 1.5. With income at 6 that forces an expenditure of 4.5, a 12.5% rise — the stem raises expenditure by 10%, giving 4.4.
• (b)
  40% — 40% would need new savings of 1.4, so an expenditure of 4.6 against income 6. That is a 15% rise in expenditure, not the 10% printed.
• (d)
  30% — 30% would need savings of 1.3, so an expenditure of 4.7 — a 17.5% rise. Subtracting the two given rates, 20% − 10%, is never the route on a residual quantity.

Savings are a residue: savings = income − expenditure. The two given percentages act on different bases, so they cannot be added or subtracted.

With expenditure : savings = 4 : 1, income is 5 parts. The 20% acts on 5 and the 10% acts on 4.

The absolute rises are 1.0 and 0.4, so savings gain 0.6 on a base of 1 — a 60% rise, even though neither given rate is anywhere near 60.

Key facts

• Income = expenditure + savings, so a 4 : 1 expenditure-to-savings ratio makes income 5 parts.
• A 20% rise on income 5 adds 1.0, while a 10% rise on expenditure 4 adds only 0.4.
• New savings of 1.6 against old savings of 1 is a 60% increase.

Common traps

• Reading 4 : 1 as income to expenditure rather than expenditure to savings
• Subtracting the rates and answering 10%
• Dividing the savings gain by the new income instead of by the old savings

No directly related past PYQ was found.