If 60% of A = 0.3 of B =1⁄6 of C, find A: B: C.

Correct — A. Call the common value k and solve for each letter.

60% of A = k → A = k ÷ 0.6 = 5k⁄3
0.3 of B = k → B = k ÷ 0.3 = 10k⁄3
1⁄6 of C = k → C = 6k

Multiply all three by 3⁄k to clear the thirds: A : B : C = 5 : 10 : 18
Check: 60% of 5 = 3, 0.3 × 10 = 3, 18 ÷ 6 = 3, all equal → option (a)

Why the others are wrong

• (b)
  18 : 10 : 5 — This is the right ratio reversed, C : B : A. Test it: 60% of 18 = 10.8, but 0.3 × 10 = 3, so the three quantities are not equal.
• (c)
  6 : 3 : 10 — Substitute it: 60% of 6 = 3.6, 0.3 × 3 = 0.9 and 10 ÷ 6 ≈ 1.67. Three different values, so the condition in the stem fails.
• (d)
  10 : 5 : 18 — It swaps A and B. Since 0.6A = 0.3B, A = B ÷ 2, so A must be the smaller. Check: 60% of 10 = 6, but 0.3 × 5 = 1.5.

When pA = qB = rC, each quantity is the common value divided by its own multiplier, so A : B : C = 1⁄p : 1⁄q : 1⁄r.

That is an inverse relation: the letter with the biggest multiplier is the smallest quantity. Here 60% is the biggest multiplier, so A is the smallest, and 1⁄6 is the smallest, so C is the largest.

The reciprocals 5⁄3, 10⁄3 and 6 then become whole numbers once you multiply by 3.

Key facts

• If pA = qB = rC, then A : B : C = 1⁄p : 1⁄q : 1⁄r.
• 60% = 0.6 = 3⁄5, so 1 ÷ 0.6 = 5⁄3.
• A ratio is checked by substituting it back: every product must come out equal.

Common traps

• Writing the multipliers themselves as the ratio: 0.6 : 0.3 : 1⁄6 scales to 18 : 9 : 5, which is direct proportion where the relation is inverse.
• Choosing the reversed ratio 18 : 10 : 5, which has the right numbers under the wrong letters.

No directly related past PYQ was found.