SSC CGL 2025 Tier-I · 12 September 2025, Shift 2 · Quantitative Aptitude · Question 10 of 100

We transcribed this text from the pictures on a candidate's response sheet for this shift; the answer is the key SSC colour-marked on that sheet. Solution last reviewed 13 September 2026.

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SSC does not publish CGL question papers or a public answer key. From 2025 the candidate response sheet prints every question and option as a picture, so the text here is transcribed from those pictures for this shift and checked against them independently; where the layout carries meaning, the picture is shown as well. Each answer is the key SSC colour-marked on that sheet. SSC released a tentative key for challenge and later its final one, both only to candidates behind a login, and the sheet does not say which of the two it carries. The solutions are written by UnlockIAS.

A candy shop owner buys three kinds of candies: red, blue, and green. Red candies are purchased at 3 for ₹15, blue candies at 4 for ₹18, and green candies at 5 for ₹22. He mixes them in the ratio 1 : 1 : 2. He sells all the mixed candies at 2 for ₹10. What is his approximate gain or loss percentage?

(a)Loss of 9.2%
(b)Profit of 9.29%
(c)Profit of 10%
(d)Loss of 10%

Answer

Why

Correct — B. Price one candy of each kind, cost one 1 : 1 : 2 set, then compare it with what the set sells for.

Red = 15 ÷ 3 = ₹5 each
Blue = 18 ÷ 4 = ₹4.50 each
Green = 22 ÷ 5 = ₹4.40 each

Cost of 1 red + 1 blue + 2 green = 5 + 4.50 + 8.80 = ₹18.30
Sale of those 4 candies at 2 for ₹10 = ₹20

Profit = 20 − 18.30 = ₹1.70
Profit % = 1.70 ÷ 18.30 × 100 ≈ 9.29% → option (b)

Why the others are wrong

(a)
Loss of 9.2% — Wrong direction. No candy costs more than ₹5 and every candy sells for ₹5, so the mix cannot make a loss. The size is close to the real 9.29% gain.
(c)
Profit of 10% — A 10% profit would need the 4-candy set to cost 20 ÷ 1.1 ≈ ₹18.18. The 1 : 1 : 2 set costs ₹18.30, so the gain falls just short, at 9.29%.
(d)
Loss of 10% — Wrong on both counts. Selling at ₹5 against an average cost of ₹4.575 is a gain, and a 10% loss would need each candy to cost about ₹5.56, dearer than the dearest (red, ₹5).

Concept

Goods bought at different rates and mixed have one cost price: a weighted average of the unit prices, weighted by how many of each go in.

The 1 : 1 : 2 ratio counts green twice, so the average is 18.30 ÷ 4 = ₹4.575 a candy, not the plain average of ₹5, ₹4.50 and ₹4.40.

Profit % is measured on that cost price: (5 − 4.575) ÷ 4.575 × 100 ≈ 9.29%.

The options come in look-alike pairs: a loss of 9.2% beside a profit of 9.29%, a profit of 10% beside a loss of 10%. Decide the direction before the size.

Key facts

Unit cost from a 'k for ₹N' rate = N ÷ k: 3 for ₹15 is ₹5 a candy.
Mixture cost price = total cost ÷ total quantity: here ₹18.30 ÷ 4 = ₹4.575.
Profit % = profit ÷ cost price × 100: 1.70 ÷ 18.30 × 100 ≈ 9.29%.

Study next

Weighted average cost of a mixtureAlligation: finding the mixing ratio from a target priceProfit and loss on 'n for ₹x' buying and selling rates

Common traps

Taking the plain average of ₹5, ₹4.50 and ₹4.40 (about ₹4.63) ignores the 2 in the ratio and gives about 7.9%.
Dividing the ₹1.70 profit by the ₹20 selling price gives 8.5%. Profit % is always on cost.

The same three-rate mix is on 14 Sep 2025, 12:30, Quant Q.15: mangoes at 4 for ₹10, 5 for ₹12 and 2 for ₹5, mixed 2 : 3 : 1, cost ₹14.70 for 6 and sell for ₹14, a loss of about 4.76%.

Notebooks mixed 3 : 4 : 3 and sold at 4 for ₹19 are on 15 Sep 2025, 16:00, Quant Q.11, where the gain works out to about 9.2%.

Related PYQs

No directly related past PYQ was found.

Topic: Profit and Loss — all 87 SSC CGL questions on it, every solved shift.