SSC CGL 2024 Tier-I · 24 September 2024, Shift 3 · Quantitative Aptitude · Question 4 of 99

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 10 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.

The income of a person is ₹16,500, and his expenditure is ₹12,000. Next year, his income increases by 24% but his expenditure decreases by 10%. The percentage increase (rounded off to the nearest integer) in his savings is:

(a)115%
(b)120%
(c)95%
(d)90%

Answer

Why

Correct — A.

Present savings = 16,500 − 12,000 = ₹4,500

New income = 16,500 × 1.24 = ₹20,460
New expenditure = 12,000 × 0.90 = ₹10,800
New savings = 20,460 − 10,800 = ₹9,660

Increase in savings = 9,660 − 4,500 = ₹5,160

Percentage rise = 5,160 ⁄ 4,500 × 100 = 114.67%
To the nearest integer, 115% → option (a).

Why the others are wrong

(b)
120% — 120% would mean new savings of ₹9,900 (4,500 × 2.2). The actual figures are ₹20,460 against ₹10,800, so savings are ₹9,660 and the rise is 114.67%.
(c)
95% — 95% would need savings of ₹8,775, which no step here produces. The rise is measured on the old savings of ₹4,500: 5,160 ⁄ 4,500 = 114.67%.
(d)
90% — This is what forgetting the expenditure cut gives. Income alone at ₹20,460 against an unchanged ₹12,000 leaves ₹8,460 and an 88% rise; the 10% cut takes expenditure to ₹10,800.

Concept

Savings are a residual — income minus expenditure — so a percentage change in savings is never the difference of the two percentage changes. Income and expenditure start from different bases.

Here the 24% rise is worth 0.24 × 16,500 = ₹3,960 and the 10% cut is worth 0.10 × 12,000 = ₹1,200. Both add to savings, and 3,960 + 1,200 = ₹5,160, exactly the increase.

The final division is against the old savings of ₹4,500, not against income, not against the new savings.

The question says rounded off to the nearest integer, so 114.67% is meant to be reported as 115%.

Key facts

Savings = income − expenditure, so a change in savings absorbs both moves at once.
A percentage rise is measured on the original value, here the old savings of ₹4,500.
24% of ₹16,500 is ₹3,960 and 10% of ₹12,000 is ₹1,200, and together they are the ₹5,160 rise.

Study next

Income, expenditure and savings problems where the data arrives as a ratioSuccessive percentage change and why two percentages cannot simply be addedChoosing the correct base for a percentage increase

Common traps

Subtracting the percentages, 24% − 10%, as though the two shared a base.
Dividing the increase by the new savings of ₹9,660 instead of the old ₹4,500.
Subtracting the ₹1,200 fall in expenditure when it actually adds to savings.

The same two levers, an income rise and an expenditure move, come back with different numbers.
25 Sep 2024, 16:00, Quant Q.7 has income ₹18,600 and expenditure ₹12,400 rising by 15% and 8%; 13 Sep 2024, 16:00, Quant Q.11 gives expenditure as 80% of income and raises the two by 15% and 5%.

Related PYQs

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