SSC CGL 2024 Tier-I · 18 September 2024, Shift 3 · Quantitative Aptitude · Question 21 of 98

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.

If A:B = 6 : 8 and B:C = 7 : 12, then A:B:C is:

(a)21:28:48
(b)21:32:40
(c)14:31:20
(d)11:23:40

Answer

Why

Correct — A. B is the shared term, but it is written as 8 in the first ratio and 7 in the second. Make it the same number in both before joining them.

LCM of 8 and 7 = 56
A : B = 6 : 8, multiplied by 7 → 42 : 56
B : C = 7 : 12, multiplied by 8 → 56 : 96

Now they chain: A : B : C = 42 : 56 : 96
Divide every term by 2 → 21 : 28 : 48

Check both givens: 21 : 28 = 3 : 4 = 6 : 8, and 28 : 48 = 7 : 12. So the answer is 21 : 28 : 48, option (a).

Why the others are wrong

(b)
21:32:40 — 21 : 32 : 40 breaks the first given. 21 : 32 is not 6 : 8, which reduces to 3 : 4 — beside A = 21 the B term has to be 28.
(c)
14:31:20 — 14 : 31 : 20 fails the same test: 14 : 31 is not 3 : 4, and 31 is prime, so no scaling of 6 : 8 can produce it.
(d)
11:23:40 — 11 : 23 : 40 cannot come from 6 : 8 either. Every ratio equivalent to 6 : 8 keeps A : B at 3 : 4, and 11 : 23 is not.

Concept

Two ratios join only through the term they share, and they must agree on it first.

The one-line rule: given A : B = a : b and B : C = c : d, write A : B : C = ac : bc : bd. Here that is 6×7 : 8×7 : 8×12 = 42 : 56 : 96.

It is the LCM method in compressed form — multiplying the first ratio by c and the second by b makes both B terms equal to bc.

Reduce at the end, never in the middle: dividing one ratio and not the other destroys the link.

You can also work backwards from the options. Each answer must satisfy both givens, so test A : B against 3 : 4 first — that alone removes every wrong option here.

Key facts

To join A : B = a : b with B : C = c : d, write A : B : C = ac : bc : bd.
6 : 8 reduces to 3 : 4, so A : B must stay 3 : 4 in any correct answer.
6×7 : 8×7 : 8×12 = 42 : 56 : 96, which reduces to 21 : 28 : 48.
21 : 28 : 48 satisfies both givens — 21 : 28 = 3 : 4 and 28 : 48 = 7 : 12.

Study next

Chaining three or more ratios, A : B, B : C and C : DCompound ratio and its use in work-and-time and speed problemsDividing a given sum among three people in a chained ratio

Common traps

Writing A : B : C = 6 : 8 : 12 by carrying B straight across, when B means 8 in one ratio and 7 in the other.
Reducing 42 : 56 : 96 by 2 but forgetting to halve one of the three terms.
Checking only A : B and marking an option whose B : C is wrong.

SSC reuses this stem almost word for word with the second ratio changed. A : B = 6 : 8 appears with B : C = 5 : 12 at 10 Sep 2024, 12:30, Quant Q.8.

The same opening runs with B : C = 5 : 10 at 13 Sep 2024, 09:00, Quant Q.18, with 7 : 10 at 17 Sep 2024, 09:00, Quant Q.3, and with 5 : 11 at 25 Sep 2024, 12:30, Quant Q.11.

Related PYQs

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