SSC CGL 2024 Tier-I · 11 September 2024, Shift 3 · Quantitative Aptitude · Question 19 of 100

Text as printed on a candidate's response sheet for this shift; answer per SSC's tentative key as marked on that sheet. Solution last reviewed 6 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. The questions and options here are reproduced as printed on a candidate's own response sheet for this shift — the Commission's text, unchanged. Each answer is SSC's tentative key as marked on that sheet; SSC allowed challenges to it and never publishes a final key. The solutions are written by UnlockIAS.

A woman spends 2⁄3 of her income. If her income increases by 18% and the expenditure increases by 24%, then the percentage increase in her savings will be:

(a)3%
(b)6%
(c)4%
(d)5%

Answer

Why

Correct — B. The stem is an image: a woman spends 2⁄3 of her income, her income rises 18% and her expenditure rises 24%.

Take income = 300, so expenditure = 200 and savings = 100
New income = 300 × 1.18 = 354
New expenditure = 200 × 1.24 = 248

New savings = 354 − 248 = 106
Rise = 6 on a base of 100 = 6% → option (b)

Why the others are wrong

(a)
3% — 3% is half the true rise. It puts savings at 103, which would need expenditure of 251 — a 25.5% jump, not the 24% the stem gives.
(c)
4% — 4% puts savings at 104, so expenditure would have to land on 250 — a 25% rise. At 24% it lands on 248, leaving savings of 106.
(d)
5% — 5% puts savings at 105, requiring expenditure of 249. Raising 200 by 24% gives 248, one unit lower, so the savings are 106 and the rise is 6%.

Concept

When income and expenditure move by different percentages, savings move by neither of them. Savings are a residual, so rebuild income and expenditure separately and subtract.

Picking numbers that make the spending fraction whole is the fastest route. Spending 2⁄3 means income 3, expenditure 2, savings 1 — scale to 300, 200 and 100 and the percentages come out in whole units.

The general form weights each rate by its share: rise in savings = (3 × 18 − 2 × 24) ÷ 1 = 6%.

6% also happens to equal 24 − 18, and that is a coincidence of this spending fraction. Change the fraction to 1⁄2 and the same two rates give 12%, so subtracting the rates is not a rule.

Key facts

Savings equal income minus expenditure, so a percentage change in savings has to be rebuilt from both.
Spending 2⁄3 of income leaves savings of 1⁄3, and that 1⁄3 is the base the 6% is measured against.
Percentage change in savings = (income share × its rate − expenditure share × its rate) ÷ savings share.

Study next

Percentage change in a residual quantity such as savings or profitChoosing a convenient base value when only a ratio is givenSuccessive percentage change applied to a single quantity

Common traps

Subtracting the two rates, 24 − 18, which returns 6 here only because the spend is 2⁄3.
Measuring the rise against the new income of 354 rather than against the old savings of 100.
Reading 2⁄3 of her income as the part saved instead of the part spent.

The same savings-residual set-up runs at 9 Sep 2024, 12:30, Quant Q.15 (spends 80%, income +20%, expenditure +10%) and at 13 Sep 2024, 16:00, Quant Q.11 (spends 80%, income +15%, expenditure +5%), where the spending share is given as a percentage rather than a fraction.

Related PYQs

No directly related past PYQ was found.