SSC CGL 2024 Tier-I · 10 September 2024, Shift 2 · Quantitative Aptitude · Question 2 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.

The concentrations of three acids, A, B, and C, are specified as 20%, 30%, and 40%, respectively. They are blended in a ratio of 3 : 5 : a, yielding a solution with a concentration of 30%. What is the value of 'a'?

(a)4
(b)1
(c)3
(d)2

Answer

Why

Correct — C. A blend's strength is total acid divided by total volume, so write both in parts.

Acid parts: 20×3 + 30×5 + 40a = 60 + 150 + 40a = 210 + 40a
Volume parts: 3 + 5 + a = 8 + a

Set the blend at 30%: (210 + 40a) ⁄ (8 + a) = 30
210 + 40a = 240 + 30a
10a = 30, so a = 3 → option (c)

Why the others are wrong

(a)
4 — a = 4 gives (210 + 160) ⁄ 12 ≈ 30.83%. Too much of the 40% acid C pushes the blend above the 30% the question fixes.
(b)
1 — a = 1 gives (210 + 40) ⁄ 9 ≈ 27.8%, below target — one part of C cannot lift a mix that is three parts of the weak 20% acid.
(d)
2 — a = 2 gives 290 ⁄ 10 = 29%, still a point short of 30%; one more part of the 40% acid closes the gap.

Concept

A mixture's concentration is the weighted average of its components, weighted by volume. That single sentence turns every acid, milk or alloy problem into one equation.

Alligation is the same statement rearranged as a balance. Acid A is 10 points below the target, acid C is 10 points above, and acid B sits exactly at the target, so B's five parts are neutral and drop out.

The deficit must equal the surplus: 3 parts × 10 below = a parts × 10 above, which gives a = 3 in one line.

Because B is already at the required 30%, the answer does not depend on B's share at all — the 5 in the ratio is there to distract.

Key facts

The strength of a blend is the volume-weighted average of the component strengths.
A component sitting exactly at the target concentration does not shift the average, whatever its share.
Alligation balances deficit against surplus about the mean: 3 × 10 = 3 × 10 here.

Study next

Alligation with the mean written between the two component valuesReplacement problems where x litres are drawn off and refilled with waterThree-component blends needing a second condition to pin two unknowns

Common traps

Averaging 20, 30 and 40 to 30 and concluding that any ratio works.
Dividing by 8 instead of 8 + a, leaving the unknown out of the denominator.
Treating a as a percentage rather than as a number of parts.

The same weighted-average set-up turns up under a different wrapper. In this shift Quant Q.17 is the profit-percentage version — 1,000 kg of sugar sold partly at 10% and partly at 40% for a 20% overall gain.

Related PYQs

No directly related past PYQ was found.