SSC CGL 2024 Tier-I · 19 September 2024, Shift 2 · Quantitative Aptitude · Question 8 of 99

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.

At a school building, there is an overhead tank. To fill this tank 50 buckets of water are required. Assume that the capacity of the bucket is reduced to two-fifth of the present. How many buckets of water are required to fill the same tank?

(a)62.5
(b)20
(c)125
(d)60

Answer

Why

Correct — C. The tank does not change, so its volume is a fixed quantity to hold on to.

Call one old bucket 1 unit.
Tank = 50 × 1 = 50 units

The new bucket holds two-fifths of the old.
New bucket = 2/5 = 0.4 unit

Buckets needed = 50 / 0.4 = 50 × 5/2 = 125 → option (c).

Why the others are wrong

(a)
62.5 — 62.5 is 50 divided by 0.8, the count if the bucket still held four-fifths of its old capacity. The stem says the capacity is reduced to two-fifths, so the divisor is 0.4.
(b)
20 — 20 is 50 × 2/5 — multiplying by the shrink factor instead of dividing by it. A smaller bucket must mean more trips, so any answer under 50 is wrong before the arithmetic starts.
(d)
60 — 60 matches no operation in the problem. It also fails the volume check: 60 buckets of 0.4 unit fill only 24 units, well under the 50 units the tank holds.

Concept

Bucket size and bucket count are in inverse proportion, because their product is the fixed volume of the tank.

So if capacity is multiplied by k, the count is divided by k. Here k = 2/5, and dividing by 2/5 is the same as multiplying by 5/2.

50 × 5/2 = 125. The direction check costs nothing: a smaller bucket needs more of them, so the answer has to exceed 50, which removes option (b) at sight.

No capacity is given in litres and none is needed. Set one old bucket to one unit, make the tank 50 units, and the whole question becomes a single division.

Key facts

For a tank of fixed volume, bucket capacity and the number of buckets are inversely proportional.
Reducing the capacity to two-fifths multiplies the number of buckets by five-halves.
50 × 5/2 = 125 buckets.
Reduced to two-fifths means the new bucket holds 40% of the old, not that 40% was taken away.

Study next

Inverse variation and the constant product xy = kTelling reduced to a fraction apart from reduced by a fraction in ratio wordingCarrying the same inverse logic into men-and-days and pipe-rate problems

Common traps

Reading reduced to two-fifths as reduced by two-fifths, which would leave three-fifths
Multiplying 50 by 2/5 instead of dividing, which gives 20
Skipping the direction check that a smaller bucket must need more trips

SSC hides inverse proportion inside everyday wording — buckets, workers, pipes — and the question turns on whether to or by precedes the fraction. The same relation is asked in bare algebraic form 9 Sep 2024, 12:30, Quant Q.22, where x varies inversely as y.

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