SSC CGL 2024 Tier-I · 9 September 2024, Shift 2 · Quantitative Aptitude · Question 5 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 5 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.

Madhav purchased an item for ₹42,000 and sold it at a loss of 20%. With that amount, he purchased another item and sold it at a gain of 30%. What is the overall gain (in ₹)?

(a)6720
(b)4200
(c)2520
(d)1680

Answer

Why

Correct — D. Follow the money through both sales.

First sale, a 20% loss on ₹42,000 returns 80% of it:
SP = 42,000 × 80⁄100 = ₹33,600

That entire ₹33,600 becomes the cost of the second item, sold at a 30% gain:
SP = 33,600 × 130⁄100 = ₹43,680

Overall gain = 43,680 − 42,000 = ₹1,680 → option (d)

One-line check: the money is multiplied by 0.8 and then by 1.3, and 0.8 × 1.3 = 1.04 — a net 4% gain, and 4% of ₹42,000 is ₹1,680.

Why the others are wrong

(a)
6720 — ₹6,720 is 16% of ₹42,000, but the two stages multiply to 0.8 × 1.3 = 1.04 — a net gain of exactly 4%, and no reading of the chain produces 16%.
(b)
4200 — The additive trap: −20% and +30% treated as +10%, and 10% of ₹42,000 is ₹4,200. Percentages taken on different bases never add — the 30% is earned on ₹33,600, not on ₹42,000.
(c)
2520 — ₹2,520 is 6% of ₹42,000, but the net effect of the two stages is 4%, which on ₹42,000 is ₹1,680.

Concept

Successive percentage changes multiply; they never add. A loss of x% is a factor of (1 − x⁄100) and a gain of y% is a factor of (1 + y⁄100).

So the whole two-stage story is a single product: 42,000 × 0.8 × 1.3 = ₹43,680. Order does not matter, since multiplication commutes — a 30% gain followed by a 20% loss lands on the same ₹43,680.

The net change is (0.8 × 1.3 − 1) × 100 = 4%, which is also what the shortcut x + y + xy⁄100 gives: −20 + 30 + (−20 × 30)⁄100 = 4.

The phrase 'with that amount' is what pins the second cost price at ₹33,600.

Had the question said he bought another item for ₹42,000, the answer would be different. That clause is doing real work and is worth re-reading before you compute.

Key facts

Successive changes of x% and y% combine into a single change of x + y + xy⁄100 per cent.
A 20% loss followed by a 30% gain is a net 4% gain, because 0.8 × 1.3 = 1.04.
Selling at a 20% loss returns 80% of cost, so ₹42,000 becomes ₹33,600.

Study next

The x + y + xy⁄100 formula applied to successive discounts and to price-then-quantity changesWhy an equal percentage gain and loss on the same article always leaves a net loss of x²⁄100 per centChains where only part of the sale proceeds is reinvested, so the second cost price must be computed separately

Common traps

Adding −20 and +30 to get a 10% gain, which lands on option (b).
Computing the 30% gain on the original ₹42,000 instead of on the ₹33,600 actually reinvested.
Answering the second item's own gain of ₹10,080 rather than the overall gain on the original outlay.

SSC states a two-stage buy-and-sell chain and asks for the overall gain, sometimes stretching it to three stages or putting a discount in place of the loss.

The wording that decides the answer is always whether the full sale proceeds carry into the next purchase.

The same multiply-the-factors idea drives Quant Q.16 of this paper, where a 26% mark-up meets a 32% discount.

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