SSC CGL 2025 Tier-I · 21 September 2025, Shift 1 · Quantitative Aptitude · Question 17 of 99

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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A chemist prepares 60 liters of antiseptic solution by mixing two liquids 'A' and 'B' in the ratio 2:3. If the cost of 'A' is Rs. 45/liter and 'B' is Rs. 30/liter, what is the average cost per liter of the final solution?

(a)Rs. 36
(b)Rs. 38
(c)Rs. 37
(d)Rs. 39

Answer

Why

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

Split 60 litres in 2 : 3: A = 60 × 2⁄5 = 24 L, B = 60 × 3⁄5 = 36 L
Cost of A: 24 × 45 = Rs. 1080
Cost of B: 36 × 30 = Rs. 1080

Total cost = Rs. 2160 for 60 L
2160 ÷ 60 = Rs. 36 per litre → option (a)

Why the others are wrong

(b)
Rs. 38 — Rs. 38 would need A and B in the ratio 8 : 7: (8 × 45 + 7 × 30) ÷ 15 = 570 ÷ 15 = 38. The given 2 : 3 has more of the cheaper B.
(c)
Rs. 37 — Rs. 37 needs the ratio 7 : 8: (7 × 45 + 8 × 30) ÷ 15 = 555 ÷ 15 = 37. The given 2 : 3 puts in even less A, so the average is lower.
(d)
Rs. 39 — Rs. 39 is the reversed ratio 3 : 2: (3 × 45 + 2 × 30) ÷ 5 = 195 ÷ 5 = 39. It gives A the 3 parts that belong to B.

Concept

The price of a mixture is a weighted average: each price counts in proportion to the quantity mixed.

With A : B = 2 : 3, A carries weight 2⁄5 and B carries 3⁄5:
(2 × 45 + 3 × 30) ÷ 5 = (90 + 90) ÷ 5 = 36

The 60 litres does not change the answer: any batch mixed 2 : 3 costs Rs. 36 per litre. The average sits nearer B's price because there is more of B.

Alligation check: the mean 36 is 9 below A's 45 and 6 above B's 30, and 6 : 9 = 2 : 3, the given A : B.

Key facts

Mixture price per unit = total cost ÷ total quantity
Weighted average of prices p and q mixed m : n = (m × p + n × q) ÷ (m + n)
Alligation: quantity of A : quantity of B = (mean − price of B) : (price of A − mean)

Study next

Alligation to find the mixing ratio for a target priceMixture problems with a profit percentage on the selling priceFinding an unknown price when the mixture price and the ratio are given

Common traps

Taking the plain average (45 + 30) ÷ 2 = 37.5, which ignores the 2 : 3 quantities
Attaching the ratio to the wrong liquid, which gives (3 × 45 + 2 × 30) ÷ 5 = 39

Two lots and find the mean price, as here, also at 17 Sep 2024, 16:00, Quant Q.14 (42 L at ₹25 and 28 L at ₹40, keyed ₹31) and 12 Sep 2024, 16:00, Quant Q.21 (5 kg at ₹4 and 3 kg at ₹6, keyed ₹4.75).

Here the quantities come as a ratio, so the 60 litres can be skipped.

Related PYQs

No directly related past PYQ was found.

Topic: Averages — all 76 SSC CGL questions on it, every solved shift.