SSC CGL 2025 Tier-I · 17 September 2025, Shift 1 · Quantitative Aptitude · Question 2 of 100

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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SSC does not publish CGL question papers or a public answer key. From 2025 the candidate response sheet prints every question and option as a picture, so the text here is transcribed from those pictures for this shift and checked against them independently; where the layout carries meaning, the picture is shown as well. Each answer is the key SSC colour-marked on that sheet. SSC released a tentative key for challenge and later its final one, both only to candidates behind a login, and the sheet does not say which of the two it carries. The solutions are written by UnlockIAS.

Given that W : X = 5 : 6, X : Y = 3 : 7, and Y : Z = 8 : 9, find the compound ratio W : X : Y : Z.

(a)20 : 24 : 56 : 63
(b)5 : 6 : 7 : 9
(c)5 : 6 : 14 : 9
(d)20 : 24 : 42 : 63

Answer

Why

Correct — A. Chain the ratios by making each shared term equal.

X is 6 in W : X and 3 in X : Y, so double X : Y
X : Y = 6 : 14, giving W : X : Y = 5 : 6 : 14

Y is 14 here and 8 in Y : Z, and their LCM is 56
Multiply W : X : Y by 4 → 20 : 24 : 56
Multiply Y : Z by 7 → 56 : 63

W : X : Y : Z = 20 : 24 : 56 : 63 → option (a)

Why the others are wrong

(b)
5 : 6 : 7 : 9 — 5 : 6 : 7 : 9 strings the given numbers together without matching the shared term. It makes X : Y = 6 : 7, but the question says 3 : 7.
(c)
5 : 6 : 14 : 9 — Y : Z = 14 : 9 in this option, not 8 : 9. W : X : Y = 5 : 6 : 14 is joined correctly, but Z was never rescaled to meet Y = 14.
(d)
20 : 24 : 42 : 63 — 42 : 63 = 2 : 3, so this option makes Y : Z = 2 : 3, not 8 : 9. Its X : Y = 24 : 42 = 4 : 7 is also wrong.

Concept

A compound (chained) ratio joins pairs that share a term. The shared term must carry the same number in both pairs before they can merge.

Scale each pair so the common term matches, usually at its LCM. Multiplying both terms of a ratio by one number leaves it unchanged, so 3 : 7 and 6 : 14 say the same thing.

Work one link at a time, and rescale everything already joined whenever the next link forces a change.

Check by reducing each adjacent pair back: 20 : 24 = 5 : 6, 24 : 56 = 3 : 7 and 56 : 63 = 8 : 9. Each matches the question.

Key facts

Multiplying both terms of a ratio by the same number leaves it unchanged.
To join A : B and B : C, make B equal in both, using the LCM of its two values.
Every adjacent pair of the final chain must reduce back to the given ratio.

Study next

End-to-end ratios such as A : D from three linksDividing an amount in a three- or four-part ratioRatios from relations such as 2A = 3B = 4C

Common traps

Rescaling only the new pair. When Y moves from 14 to 56, W and X must be multiplied by 4 as well.
Reading the numbers straight off the question (5 : 6 : 7 : 9) without matching the shared term.

The same chaining settles 14 Sep 2025, 12:30, Quant Q.1, which asks for N : P from three links (answer 54 : 77). A two-link version is 10 Sep 2024, 12:30, Quant Q.8: A : B = 6 : 8 and B : C = 5 : 12 give 15 : 20 : 48.

Related PYQs

No directly related past PYQ was found.

Topic: Ratio & Proportion — all 96 SSC CGL questions on it, every solved shift.