If A:B = 6 : 8 and B:C = 5 : 11, then A:B:C is:

Correct — C. Two ratios join only through the term they share, so make B the same number in both.

A : B = 6 : 8 and B : C = 5 : 11
LCM of the two B terms, 8 and 5, is 40
Scale the first ratio by 5 → A : B = 30 : 40
Scale the second by 8 → B : C = 40 : 88

A : B : C = 30 : 40 : 88, and halving every term gives 15 : 20 : 44 → option (c)

Why the others are wrong

• (a)
  14:31:25 — 14 : 31 : 25 — A : B = 6 : 8 reduces to 3 : 4, so A must be three-quarters of B. Here 14 is under half of 31, and the first ratio already fails.
• (b)
  15:32:44 — 15 : 32 : 44 — the outer terms are right, but this makes B : C = 32 : 44 = 8 : 11, not the 5 : 11 the question gives. Only the middle term is wrong.
• (d)
  11:23:14 — 11 : 23 : 14 — B : C = 5 : 11 forces C to be more than double B. This option puts C at 14, smaller than B at 23, so it fails on sight.

A : B and B : C both name B, but with different numbers — 8 in one, 5 in the other. Until B is written the same way in both, the two ratios cannot be read against each other.

Multiplying every term of a ratio by the same non-zero number leaves it unchanged. So multiply the first ratio by the second's B term and the second by the first's B term, or use their LCM, which keeps the numbers small.

Reduce only at the end. 30 : 40 : 88 is a correct answer, but the printed one is its halved form.

Key facts

• To combine A : B with B : C, scale each until the two B terms agree.
• 6 : 8 and 5 : 11 combine to 30 : 40 : 88, which halves to 15 : 20 : 44.
• A ratio is unchanged when every term is multiplied or divided by the same non-zero number.

Common traps

• Multiplying straight across as 6 × 5 : 8 × 11 without first matching the two B terms
• Reducing 30 : 40 : 88 before the third term has been attached
• Verifying only A : B and stopping, which lets option (b) through

No directly related past PYQ was found.