SSC CGL 2025 Tier-I · 15 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 A : B = 7 : 5, B : C = 2 : 3, and C : D = 4 : 5, find the ratio A : D.

(a)14 : 25
(b)28 : 25
(c)56 : 75
(d)75 : 56

Answer

Why

Correct — C. Multiply the three ratios as fractions, because the linking terms B and C cancel.

Write as fractions: A⁄D = 7⁄5 × 2⁄3 × 4⁄5
Multiply numerators: 7 × 2 × 4 = 56
Multiply denominators: 5 × 3 × 5 = 75
So A : D = 56 : 75 → option (c)

Why the others are wrong

(a)
14 : 25 — 14 : 25 scales to 42 : 75, a smaller share for A than the chain allows. The product of the three ratios is 56⁄75, not 42⁄75.
(b)
28 : 25 — 28 : 25 scales to 84 : 75 and would make A larger than D. The chain gives 56⁄75, which is below 1, so A is the smaller quantity.
(d)
75 : 56 — 75 : 56 is the right pair in the wrong order: it is D : A. The question asks for A : D, so A's figure, 56, comes first.

Concept

A ratio chain links quantities through the terms they share. In A : B, B : C and C : D, B and C are the links: written as fractions, (A⁄B) × (B⁄C) × (C⁄D) = A⁄D.

The longer route makes each link equal in turn. A : B = 14 : 10 and B : C = 10 : 15 give A : B : C = 14 : 10 : 15. Scaling that by 4, and C : D = 4 : 5 by 15, puts C at 60 in both: A : B : C : D = 56 : 40 : 60 : 75.

Check against every given ratio. In 56 : 40 : 60 : 75, A : B = 56 : 40 = 7 : 5, B : C = 40 : 60 = 2 : 3 and C : D = 60 : 75 = 4 : 5, so 56 : 75 is consistent with all three.

Key facts

Written as fractions, A⁄B × B⁄C × C⁄D = A⁄D.
To combine two ratios, make the shared term equal: 7 : 5 and 2 : 3 become 14 : 10 and 10 : 15.
A : D and D : A use the same two numbers in opposite order.

Study next

Combining A : B and B : C into a three-term ratio A : B : CCompound ratio: multiplying ratios term by termFinding one quantity from a chained ratio and a given total

Common traps

Writing A : B : C as 7 : 5 : 3 without first making B equal — B is 5 in one ratio and 2 in the other.
Answering D : A: 75 : 56 is the answer reversed.

Making the shared term equal also decides 13 Sep 2024, 09:00, Quant Q.18, where A : B = 6 : 8 and B : C = 5 : 10 combine to 3 : 4 : 8.

17 Sep 2024, 09:00, Quant Q.3 uses A : B = 6 : 8 and B : C = 7 : 10: B becomes 56 in both, giving 21 : 28 : 40.

Related PYQs

No directly related past PYQ was found.

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