SSC CGL 2024 Tier-I · 12 September 2024, Shift 2 · Quantitative Aptitude · Question 16 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.

Every month, a man consumes 20 kg of rice and 8 kg of wheat. The price of rice is 20% of the price of wheat, resulting in a total expenditure of ₹300 per month for rice and wheat combined. If the price of wheat is increased by 20%, what percentage reduction in rice consumption is needed to maintain the same expenditure of ₹300? (Given that price of rice and consumption of wheat is constant.)

(a)24%
(b)22%
(c)40%
(d)38%

Answer

Why

Correct — C. Let wheat cost w per kg, so rice costs 0.2w.

20(0.2w) + 8w = 300 → 4w + 8w = 300
12w = 300, so wheat = ₹25 and rice = ₹5 per kg
Old split: rice 20 × 5 = ₹100, wheat 8 × 25 = ₹200

Wheat rises 20% to ₹30, and the same 8 kg now costs ₹240
Rice is left 300 − 240 = ₹60, which at ₹5 buys 12 kg
Cut = (20 − 12) ⁄ 20 = 40% → option (c)

Why the others are wrong

(a)
24% — A 24% cut leaves 15.2 kg of rice, costing ₹76. With wheat now at ₹240 the bill is ₹316 — ₹16 over the ₹300 the man must hold to.
(b)
22% — A 22% cut leaves 15.6 kg at ₹78, and ₹240 + ₹78 = ₹318. The rice budget has to fall all the way to ₹60, not merely dip.
(d)
38% — Close, but 38% leaves 12.4 kg costing ₹62, and ₹240 + ₹62 = ₹302. The rice quota is ₹60 exactly, which is a 40% cut.

Concept

Two quantities are held fixed and the stem says so: the price of rice and the quantity of wheat. That makes this a budget split, not a percentage identity.

Recover the two prices from the ₹300 bill, split that bill into a rice part and a wheat part, then let the wheat part swell by 20%. What is left is the new rice budget — and because the rice price has not moved, the quantity falls in exactly the same proportion as that budget.

'The price of rice is 20% of the price of wheat' is a price relation, not a spending one. Rice still ends up at ₹100 of the ₹300 because 20 kg is a large quantity of a cheap grain, and wheat takes the other ₹200.

Key facts

Wheat works out at ₹25 per kg and rice at ₹5 per kg, which is 20% of the wheat price.
The original ₹300 splits as ₹100 on rice and ₹200 on wheat.
A 20% rise lifts the wheat bill from ₹200 to ₹240, leaving ₹60 for rice.

Study next

Expenditure problems where price rises and consumption is cut to hold the billPercentage change in one component of a fixed total budgetTurning a price ratio into an expenditure ratio using the quantities

Common traps

Cutting rice by 20% because wheat rose 20%, which ignores the sizes of the two budgets.
Applying the 20% rise to the whole ₹300 instead of to the wheat share alone.
Reversing the relation and making wheat 20% of the price of rice.

SSC also asks the mirror version, where the consumption cut is given and the change in the bill is wanted.

At 19 Sep 2024, 09:00, Quant Q.17 the tomato price rises 300%, the housewife cuts consumption 70%, and the question is what happens to her expenditure.

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