SSC CGL 2024 Tier-I · 17 September 2024, Shift 3 · Quantitative Aptitude · Question 14 of 98

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.

42 litres of milk at ₹25 per litre is mixed with 28 litres of milk at ₹40 per litre. Find the average price of the mixture.

(a)₹31
(b)₹32
(c)₹31.5
(d)₹32.5

Answer

Why

Correct — A. Average price of a mixture = total cost ÷ total quantity.

Cost of the cheaper lot: 42 × 25 = ₹1,050
Cost of the dearer lot: 28 × 40 = ₹1,120

Total cost = 1,050 + 1,120 = ₹2,170
Total volume = 42 + 28 = 70 litres

2,170 ⁄ 70 = ₹31 per litre → option (a).
Alligation agrees: 42 : 28 is 3 : 2, and (3 × 25 + 2 × 40) ⁄ 5 = 155 ⁄ 5 = 31.

Why the others are wrong

(b)
₹32 — ₹32 implies a total of 32 × 70 = ₹2,240 for the mixture. The two lots actually cost ₹2,170, so this sits ₹70 above the money in the question.
(c)
₹31.5 — ₹31.5 implies a total of 31.5 × 70 = ₹2,205, which is ₹35 more than the ₹2,170 the two lots cost. The division 2,170 ⁄ 70 is exact and lands on 31.
(d)
₹32.5 — ₹32.5 is the plain midpoint of ₹25 and ₹40 — the answer if the two lots were equal in volume. They are 42 and 28 litres, so the cheaper rate pulls the mean below the midpoint.

Concept

The average price of a mixture is a weighted mean: every litre is counted once, so the rate attached to more litres pulls harder.

Total cost over total quantity always works. Alligation is the same calculation rearranged: the two rates and the mean sit on a line, and the distances from the mean come out in the inverse ratio of the quantities. Here 42 : 28 in volume gives distances 6 : 9, that is 2 : 3.

Both liquids are milk, so nothing is being diluted and no free water enters the total cost. The item is pure weighted averaging with no second stage.

Key facts

Average price of a mixture = total cost ÷ total quantity, not the plain average of the two rates.
42 : 28 reduces to 3 : 2, so the mean is (3 × 25 + 2 × 40) ⁄ 5 = ₹31.
A weighted mean always lies between the two rates and nearer the rate carrying the larger quantity.
The alligation distances 31 − 25 = 6 and 40 − 31 = 9 stand in ratio 2 : 3, the inverse of the 3 : 2 volumes.

Study next

Alligation used in reverse — the mean price is given and the mixing ratio is askedAdding water to milk and its effect on cost price per litreWeighted average across three or more lots at different rates

Common traps

Averaging ₹25 and ₹40 to ₹32.5 and ignoring that the volumes differ.
Writing the alligation distances in the same order as the quantities. They come out inverted, so 3 : 2 in volume gives 2 : 3 in distance.
Multiplying 42 by 40 and 28 by 25, which swaps the rates and returns ₹34 instead.

Two lots and find the mean, as here, also at 12 Sep 2024, 16:00, Quant Q.21 (5 kg and 3 kg of sugar at ₹4 and ₹6) and 13 Sep 2024, 09:00, Quant Q.5 (rice mixed 7 : 8).

The same machinery is run backwards, with the mean given and something else asked — the quantity to add at 26 Sep 2024, 16:00, Quant Q.9, the missing rate at 19 Sep 2024, 09:00, Quant Q.2.

Related PYQs

No directly related past PYQ was found.