SSC CGL 2025 Tier-I · 16 September 2025, Shift 1 · Quantitative Aptitude · Question 1 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.

If P : Q = 6 : 11, Q : R = 5 : 4, and R : S = 9 : 7, find P : Q : R : S.

(a)270 : 495 : 396 : 308
(b)6 : 11 : 4 : 7
(c)30 : 55 : 44 : 35
(d)270 : 396 : 495 : 308

Answer

Why

Correct — A. Make the shared term equal at each link of the chain.

Q is 11 in P : Q and 5 in Q : R, so LCM = 55
P : Q × 5 = 30 : 55
Q : R × 11 = 55 : 44
So P : Q : R = 30 : 55 : 44

R is 44 here and 9 in R : S, so LCM = 396
P : Q : R × 9 = 270 : 495 : 396
R : S × 44 = 396 : 308
So P : Q : R : S = 270 : 495 : 396 : 308 → option (a)

Why the others are wrong

(b)
6 : 11 : 4 : 7 — 6 : 11 : 4 : 7 just strings the given numbers together. It makes Q : R = 11 : 4, but the stem gives Q : R = 5 : 4, because Q was never matched.
(c)
30 : 55 : 44 : 35 — The first three terms are right (30 : 55 : 44), but R : S was never scaled. 44 : 35 is not 9 : 7, since 44 × 7 = 308 and 35 × 9 = 315.
(d)
270 : 396 : 495 : 308 — It swaps Q and R. Here Q : R = 396 : 495 = 4 : 5, the reverse of the given 5 : 4, and P : Q = 270 : 396 is not 6 : 11.

Concept

A chain of ratios can be joined only through the term two ratios share. Scale each ratio so the shared term takes the same value, the LCM of its two values, and the other terms move in proportion.

With four quantities the join happens twice over: first on Q, then on R. Scaling R also means scaling everything already joined to it, so P and Q are multiplied by 9 along with R.

Check any answer by reducing each adjacent pair: 270 : 495 = 6 : 11, 495 : 396 = 5 : 4 and 396 : 308 = 9 : 7. All three must hold at once.

Key facts

For A : B = a : b, B : C = c : d and C : D = e : f, A : B : C : D = ace : bce : bde : bdf.
Here that gives 6×5×9 : 11×5×9 : 11×4×9 : 11×4×7 = 270 : 495 : 396 : 308.
Multiplying both terms of a ratio by the same number leaves the ratio unchanged.

Study next

Three-term ratios A : B : C built from A : B and B : CDividing an amount among four people in a continued ratioCompound ratio of two ratios (a : b and c : d give ac : bd)

Common traps

Writing the given numbers side by side, as in 6 : 11 : 4 : 7, without matching the shared terms.
Scaling R : S but forgetting to scale P and Q by the same factor.
Swapping two middle terms while scaling, which turns Q : R = 5 : 4 into 4 : 5.

Each option is a complete P : Q : R : S chain, so check every adjacent pair against the stem. The same four-term construction appears at 17 Sep 2025, 09:00, Quant Q.2, with W : X = 5 : 6, X : Y = 3 : 7 and Y : Z = 8 : 9.

Related PYQs

No directly related past PYQ was found.

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