SSC CGL 2024 Tier-I · 13 September 2024, Shift 1 · Quantitative Aptitude · Question 18 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 10 September 2026.

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If A:B = 6 : 8 and B:C = 5 : 10, then A:B:C is:

(a)1:2:4
(b)3:4:8
(c)4:3:2
(d)1:3:4

Answer

Why

Correct — B. B carries a different number in each ratio — 8 in the first, 5 in the second — so scale both until it matches.

A:B = 6:8, multiply through by 5 → 30:40
B:C = 5:10, multiply through by 8 → 40:80

B is now 40 in both, so the two chain directly:
A:B:C = 30:40:80

Divide by 10 → 3:4:8, which is option (b).

Why the others are wrong

(a)
1:2:4 — Takes 1:2 from B:C and reuses it for A:B as well. The paper gives A:B = 6:8, which reduces to 3:4, not 1:2, so A is understated against B.
(c)
4:3:2 — A is smaller than B in the given 6:8, and C is larger than B in 5:10. A falling chain 4:3:2 reverses both relations, so it fails before any arithmetic is needed.
(d)
1:3:4 — Its A:B is 1:3, but the paper gives A:B = 6:8 = 3:4. Its B:C works out to 3:4 as well, which contradicts the given B:C = 5:10 = 1:2.

Concept

Two ratios can only be joined through the term they share, and here that term is B — named in both, but with different numbers.

Scale each ratio so B becomes the same value in each. The LCM of 8 and 5 is 40, so multiply the first ratio by 5 and the second by 8. B then reads 40 on both sides and the three terms line up as 30:40:80.

Reduce only at the end. Reducing 6:8 to 3:4 first is legal, but it does not by itself let you chain — the B terms still have to be made equal.

The numbers are picked so that careless reduction still looks plausible: 6:8 and 5:10 both collapse to neat forms, 3:4 and 1:2, which is exactly what makes 1:2:4 tempting.

Key facts

To join A:B and B:C, scale both until B is the same number in each — use the LCM of the two B values.
A:B = 6:8 reduces to 3:4.
B:C = 5:10 reduces to 1:2.
Scaled to a common B of 40, A:B:C = 30:40:80, which reduces to 3:4:8.

Study next

Chaining three or more ratios through a shared term (A:B, B:C, C:D)Dividing a sum of money in a compound ratio such as 3:4:8Turning a ratio into a fraction of the whole, e.g. A as 3/15 of A + B + C

Common traps

Reducing each ratio separately and writing the reduced terms side by side, which throws away the scaling that makes B match.
Assuming the shape of B:C also applies to A:B, which produces 1:2:4.
Reducing 30:40:80 by 5 instead of 10 and answering 6:8:16, an unreduced form of the same ratio.

SSC keeps this to a single step: two ratios sharing a middle term, with the options already reduced, so the whole item is the scaling move. Ratio work also drives Quant Q.2 (cost price to selling price at 250% profit) and Quant Q.5 (two rices mixed in 7 : 8) of the 13 Sep 2024, 09:00 paper.

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