SSC CGL 2024 Tier-I · 10 September 2024, Shift 2 · Quantitative Aptitude · Question 8 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 6 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 = 5 : 12, then A:B:C is:

(a)10:23:14
(b)11:32:44
(c)14:31:28
(d)15:20:48

Answer

Why

Correct — D. Make B the same number in both ratios, then read all three terms off together.

A : B = 6 : 8 and B : C = 5 : 12
B is 8 in the first and 5 in the second; LCM(8, 5) = 40

Multiply the first by 5: A : B = 30 : 40
Multiply the second by 8: B : C = 40 : 96

So A : B : C = 30 : 40 : 96
Divide throughout by 2: 15 : 20 : 48 → option (d)

Why the others are wrong

(a)
10:23:14 — In 10 : 23 : 14 the first two terms give A : B = 10 : 23, which is no scaling of 6 : 8, and C comes out smaller than B.
(b)
11:32:44 — 11 : 32 : 44 breaks the second link: B : C = 32 : 44 reduces to 8 : 11, while the question fixes B : C = 5 : 12.
(c)
14:31:28 — In 14 : 31 : 28 the last term is smaller than B, but B : C = 5 : 12 makes C more than twice B.

Concept

Two ratios sharing a term are joined by scaling until that shared term matches. B appears as 8 in A : B and as 5 in B : C, so scale both to the LCM of 8 and 5, which is 40.

Multiplying every term of a ratio by the same non-zero number leaves the ratio unchanged, which is why 30 : 40 : 96 and 15 : 20 : 48 say exactly the same thing.

A faster check on multiple choice: any correct option must have its first two terms in the ratio 3 : 4 and its last two in 5 : 12. Only one option survives both tests.

Key facts

To combine A : B with B : C, scale each so that B is the LCM of the two B-terms.
A ratio is unchanged when every term is multiplied or divided by the same non-zero number.
In the answer 15 : 20 : 48, the first pair reduces to 3 : 4 (= 6 : 8) and the second pair is 20 : 48 = 5 : 12.

Study next

Chaining three or more ratios: A : B, B : C and C : DConverting a ratio into actual values once a total is givenRatios in partnership problems, where shares of profit follow capital and time

Common traps

Writing A : B : C = 6 : 8 : 12 by carrying C straight across, ignoring that B is 8 in one ratio and 5 in the other.
Reducing 6 : 8 to 3 : 4 first and then losing track of the factor needed for C.
Stopping at 30 : 40 : 96 and not recognising it as the option 15 : 20 : 48.

The options here are in lowest terms, so a candidate who reaches 30 : 40 : 96 has to divide before looking for it. The same shift's Quant Q.9 takes the next step and compares one figure against an average.

Related PYQs

No directly related past PYQ was found.