SSC CGL 2024 Tier-I · 23 September 2024, Shift 1 · Quantitative Aptitude · Question 14 of 97

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.

Amit and Bilal buy goods for ₹1,500 and ₹2,000, respectively. Amit marks his goods up by y%, while Bilal marks his goods up by 2y% and offers a discount of y%. If both make the same profit, then find the value of y.

(a)10.5
(b)12.5
(c)11.5
(d)12

Answer

Why

Correct — B. Amit only marks up, so his profit is 1500 × y⁄100 = 15y.

Bilal's marked price = 2000(1 + 2y⁄100) = 2000 + 40y
After the y% discount, SP = (2000 + 40y)(1 − y⁄100)
= 2000 + 40y − 20y − 0.4y² = 2000 + 20y − 0.4y²
Bilal's profit = SP − 2000 = 20y − 0.4y²

Equal profits: 15y = 20y − 0.4y²
0.4y² = 5y, so y = 5 ⁄ 0.4 = 12.5 → option (b).

Check: Amit makes 12.5% of 1500 = ₹187.50; Bilal sells at 2500 × 0.875 = ₹2,187.50, also ₹187.50 of profit.

Why the others are wrong

(a)
10.5 — At y = 10.5 Bilal earns ₹165.90 against Amit's ₹157.50. Bilal is still ahead, so the profits are not yet equal.
(c)
11.5 — y = 11.5 leaves Bilal on ₹177.10 and Amit on ₹172.50. The gap has narrowed but has not closed.
(d)
12 — y = 12 is the near miss: Bilal makes ₹182.40, Amit ₹180. Equality arrives only at 12.5.

Concept

A markup followed by a discount is not the two percentages netted off, because the discount is taken on the marked price, not on the cost. Write it multiplicatively:
SP = CP × (1 + m⁄100) × (1 − d⁄100).

Expanding leaves a −md⁄10000 cross term. That is why Bilal's '2y% up, y% off' is worth a net markup of only y − 2y²⁄100 percent, not y percent — and it is the term the whole question turns on.

Both cost prices matter and neither cancels.

Note that the question equates profit amounts, not percentages. Equating the percentages instead would give y = y − 2y²⁄100, whose only solution is y = 0.

Key facts

Successive markup and discount multiply: SP = CP × (1 + m⁄100) × (1 − d⁄100).
A markup of 2y% followed by a discount of y% leaves a net markup of (y − 2y²⁄100) percent.
Profit is always measured against cost price, not marked price.
At y = 12.5 both men make ₹187.50, but that is 12.5% for Amit and 9.375% for Bilal.

Study next

Two successive discounts and the single equivalent discountRelating cost price, marked price and selling price when markup and discount both actForming a quadratic from an equal-profit condition and discarding the zero root

Common traps

Treating '2y% up then y% off' as a net y% markup and losing the quadratic entirely.
Cancelling y without noting that y = 0 is the discarded root of 0.4y² = 5y.
Equating profit percentages when the question equates profit amounts.

SSC moves the unknown around inside the same markup-and-discount frame.

Cost given as 75% of marked price, gain wanted after a 15% discount, at Quant Q.19 of 11 Sep 2024, 12:30. Four rival discount schemes set against each other at Quant Q.18 of this paper (23 Sep 2024, 09:00), which asks which of them sells cheapest.

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