If 15% of A is double of 30% of B, then what is the ratio of A to B?

Correct — D, 4 : 1. Turn the sentence into an equation exactly as written: fifteen per cent of A is double thirty per cent of B, so 0.15A = 2 × 0.30B, that is 0.15A = 0.60B. Divide both sides by 0.15 and A = 4B, so A : B = 4 : 1. The same thing in fractions avoids decimals altogether: (15/100)A = 2 × (30/100)B gives 15A = 60B, and dividing by 15 gives A = 4B. A quick sanity check with numbers seals it — put B = 1 and A = 4; thirty per cent of 1 is 0.3, double that is 0.6, and fifteen per cent of 4 is also 0.6.

• (a)1 : 2 — This would need 0.15A = 0.075B, which is nowhere in the statement. The ratio is inverted and shrunk at the same time.
• (b)2 : 1 — The trap for anyone who drops the word 'double'. If 15% of A merely equalled 30% of B then A would be 2B; the doubling makes it 4B.
• (c)1 : 4 — The right numbers the wrong way round. Because A carries the smaller percentage and still has to reach twice the larger one, A must be the bigger quantity, not the smaller.

A percentage statement is a multiplication, and a ratio question about two quantities is just that multiplication rearranged. Write x per cent of A as (x/100)A, put the whole sentence into one equation, and then collect A on one side. Clearing the hundreds immediately is the habit worth building, because it turns every such item into small whole-number arithmetic.

Two things decide this item and both are about reading. First, the word 'double' attaches to the right-hand side, so it multiplies the thirty per cent of B and not the fifteen per cent of A. Second, the direction of the ratio: the option list deliberately offers both 4 : 1 and 1 : 4. A one-line reasonableness check settles the direction without algebra — A is being taken at a smaller rate yet has to come out larger, so A itself must be the larger quantity.

• The statement translates to 0.15A = 2 × 0.30B, that is 15A = 60B.
• Dividing by 15 gives A = 4B, so A : B is 4 : 1.
• Clearing the denominators of 100 at the first step removes all decimals from the working.
• A check with B = 1 and A = 4 gives 0.6 on both sides.
• When the quantity carrying the smaller percentage has to match a larger amount, that quantity must be the bigger of the two.

• Ignoring the word 'double' and answering 2 : 1.
• Reporting the ratio the wrong way round as 1 : 4.
• Working in decimals and mislaying a factor of ten between 0.15 and 0.6.

Asked as a one-line percentage-to-ratio translation, with both the correct ratio and its reverse offered so that careless reading is punished.

• practice — not a real PYQ

  If 40% of A is equal to 60% of B, then A : B is

  • (a)2 : 3
  • (b)3 : 2
  • (c)1 : 2
  • (d)2 : 1

  Answer(b) 3 : 2 — 40A = 60B gives 2A = 3B, so A : B = 3 : 2.

• practice — not a real PYQ

  If 25% of X is half of 20% of Y, then X : Y is

  • (a)2 : 5
  • (b)5 : 2
  • (c)1 : 2
  • (d)2 : 1

  Answer(a) 2 : 5 — 25X = 10Y gives 5X = 2Y, so X : Y = 2 : 5.