SSC CGL 2024 Tier-I · 23 September 2024, Shift 2 · Quantitative Aptitude · Question 4 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 10 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.

Find the fourth proportional to 4, 9 and 16.

(a)36
(b)18
(c)16
(d)27

Answer

Why

Correct — A. Rule: the fourth proportional to a, b, c is the x that makes a : b :: c : x, so x = b × c ⁄ a.

Here a = 4, b = 9, c = 16.

x = 9 × 16 ⁄ 4
= 144 ⁄ 4 = 36 → option (a)

Check both ratios: 4 : 9 and 16 : 36 each reduce to 4 : 9, because 16 and 36 are 4 times 4 and 4 times 9.

Why the others are wrong

(b)
18 — 18 doubles the middle term. But going from 4 to 16 multiplies by 4, so 9 must be multiplied by 4 too — 16 : 18 reduces to 8 : 9, not 4 : 9.
(c)
16 — 16 just repeats the third term, which would make the last ratio 1 : 1 while the first is 4 : 9. A fourth proportional equals the third term only when the first two are equal.
(d)
27 — 27 triples the 9, a multiplier that appears nowhere in the data. The scale factor is set by 16 ⁄ 4 = 4, and 16 : 27 does not reduce to 4 : 9.

Concept

Four quantities are in proportion when a : b :: c : x, which is the same as saying ax = bc — the product of the extremes equals the product of the means.

Solve that for the missing extreme and you get x = bc ⁄ a. The word 'fourth' just tells you which of the four slots is empty.

Three named cases share the vocabulary and are constantly swapped by candidates: the fourth proportional to a, b, c is bc ⁄ a, the third proportional to a and b is b² ⁄ a, and the mean proportional between a and b is √(ab).

The order of the three given numbers matters. Read them as first, second, third — 4, then 9, then 16.

Swap the first two and you are solving 9 : 4 :: 16 : x, which gives x = 4 × 16 ⁄ 9 = 64⁄9. Every option here is a whole number, so a fractional answer is the sign that the terms have been read out of order.

Key facts

The fourth proportional to a, b, c is bc ÷ a.
The third proportional to a and b is b² ÷ a.
The mean proportional between a and b is the square root of ab.
Here 9 × 16 ÷ 4 = 36, and 16 : 36 reduces to 4 : 9.

Study next

Mean proportional and third proportional, and how each differs from the fourthContinued proportion a : b :: b : c, and finding the middle termCompound ratio and duplicate ratio, where the same extremes-and-means idea returns

Common traps

Taking the square root because the word proportional triggers the mean-proportional formula
Computing ab ÷ c instead of bc ÷ a
Reading the three numbers out of the order the stem gives them

The proportion vocabulary is what SSC varies — which of the three proportionals the one-line stem asks for.

The mean proportional is asked 23 Sep 2024, 09:00, Quant Q.15 (30 is the mean proportional of 18 and A) and 12 Sep 2024, 16:00, Quant Q.18 (the mean proportional of 2 and 32).

Related PYQs

No directly related past PYQ was found.