SSC CGL 2024 Tier-I · 10 September 2024, Shift 3 · Quantitative Aptitude · Question 23 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.

A shopkeeper allows a discount of 20% on the marked price of an item and thus gains 10%. What is the ratio of the cost price to the marked price of the item?

Answer

Why

Correct — D. One selling price, written two ways.

From the marked price: SP = MP × (100 − 20)⁄100 = 0.8 MP
From the cost price: SP = CP × (100 + 10)⁄100 = 1.1 CP

Set them equal: 0.8 MP = 1.1 CP

CP⁄MP = 0.8⁄1.1 = 8⁄11
So CP : MP = 8 : 11 → option (d).

Sanity check with MP = 100: SP = 80, and 80 is 110% of 800⁄11 ≈ 72.7.

Why the others are wrong

(a)
Gives a gain of 15.6%, not 10%. At CP : MP = 9 : 13 the discounted price 0.8 MP is 0.8 × 13⁄9 = 1.156 times the cost.
(b)
Gives a gain of 14.3%. A cost of 0.7 MP against a selling price of 0.8 MP is 0.8 ÷ 0.7 = 1.143 times the cost, well above the 10% fixed by the stem.
(c)
Gives a gain of barely 1.8%: 11⁄14 ≈ 0.786, and 0.8 ÷ 0.786 = 1.018. The ratio has to be 0.8 ÷ 1.1, which reduces to 8 : 11.

Concept

Discount is reckoned on the marked price, profit on the cost price. The selling price is the one number both sentences describe, so it is the bridge.

SP = MP(1 − d) and SP = CP(1 + p), which rearranges to CP⁄MP = (1 − d)⁄(1 + p).

Here (1 − 0.20)⁄(1 + 0.10) = 80⁄110 = 8⁄11. Because the answer is a ratio, no rupee figure is ever needed.

Assuming MP = ₹100 is the fastest route, but keep the cost as the exact fraction 800⁄11 rather than rounding it to ₹72.73.

A rounded cost turns a clean 8 : 11 into a decimal you then have to match against four exact ratios.

Key facts

CP⁄MP = (100 − discount%)⁄(100 + profit%).
Here CP⁄MP = 80⁄110 = 8⁄11.
Discount is always calculated on the marked price and profit always on the cost price.

Study next

Successive discounts and the single equivalent discountFixing the marked price above cost so a stated discount still leaves a target profitProfit questions where the shopkeeper also uses a false weight

Common traps

Computing MP : CP = 11 : 8 and reading it in the order the question did not ask for.
Taking 20% off and adding 10% back on the same base, as if both sat on the marked price.
Treating 'gains 10%' as 10% of the marked price.

SSC rotates the unknown around the single equation MP(1 − d) = CP(1 + p) — sometimes the discount, sometimes the profit, sometimes the ratio.

The same shift runs the successive-discount version at Quant Q.3, where ₹1,000 marked is cut by 20%, 30% and 10% in turn.

Related PYQs

No directly related past PYQ was found.