SSC CGL 2024 Tier-I · 24 September 2024, Shift 2 · Quantitative Aptitude · Question 21 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 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.

An article is sold for ₹747 after successive discounts of 17% and x%. If the marked price of the article is₹1,600, what is the value of x?

(a)40.28
(b)32.26
(c)43.75
(d)22.12

Answer

Why

Correct — C. Marked price ₹1,600, first discount 17%, second discount x%, selling price ₹747.

After the first discount:
1600 × (100 − 17)⁄100 = 1600 × 0.83 = ₹1,328

The second discount acts on ₹1,328, not on ₹1,600:
1328 × (100 − x)⁄100 = 747
(100 − x)⁄100 = 747⁄1328 = 0.5625

100 − x = 56.25
x = 43.75 → option (c)

Why the others are wrong

(a)
40.28 — Substituting x = 40.28 gives 1328 × 0.5972 ≈ ₹793, well above the ₹747 the stem states. Any second discount smaller than 43.75% leaves too much price standing.
(b)
32.26 — x = 32.26 gives 1328 × 0.6774 ≈ ₹899.59. The stem fixes the selling price at ₹747, which is under half the marked price, so a second cut this small cannot reach it.
(d)
22.12 — x = 22.12 leaves 1328 × 0.7788 ≈ ₹1,034, nowhere near ₹747. Falling from ₹1,600 to ₹747 is a drop of 53.31%, and 17% with 22.12% compound to only about 35%.

Concept

Successive discounts compound downwards: the second is taken on what survives the first, never on the marked price.

Two equivalent routes. Multiply the survival fractions, 1600 × 0.83 × (1 − x⁄100) = 747.

Or use the single-equivalent form: discounts of a% and b% together equal a + b − ab⁄100 per cent.

Here the total drop is (1600 − 747)⁄1600 = 53.3125%, and that is not 17 + x. Adding the two rates instead of compounding them is the standard slip: 17 + 43.75 = 60.75, not 53.31.

The numbers are cleaner as fractions. 747⁄1328 reduces to 9⁄16 because both are multiples of 83, so the second survival fraction is exactly 0.5625 and x = 43.75 with no decimal work at all.

Key facts

Two successive discounts of a% and b% equal a single discount of a + b − ab⁄100 per cent.
17% and 43.75% combine to 17 + 43.75 − 7.4375 = 53.3125%, and 1600 × (1 − 0.533125) = 747.
The second discount is computed on the reduced price ₹1,328, not on the marked price ₹1,600.
747⁄1328 = 9⁄16 = 0.5625, so the second discount is 43.75%.

Study next

Single equivalent discount for two and for three successive reductionsWorking backwards from a selling price to an unknown discount rateMarked price, discount and profit chained in one sum

Common traps

Applying the second discount to ₹1,600 instead of to ₹1,328.
Adding 17 and x to match the 53.31% total drop, which returns 36.31 rather than 43.75.
Rounding 0.5625 to 0.56 early, which shifts x to about 44 and off the option list.

SSC runs successive discounts in both directions. Given both rates and asked for the price: 23 Sep 2024, 12:30, Quant Q.11. Given the price and one rate and asked for the missing rate, as here: 18 Sep 2024, 12:30, Quant Q.3.

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