Two different quantities of the same solution having ingredients A and B are stored in two different containers. In the first container, there are 252 litre of A and 441 litre of B. In the second container, the total quantity of the solution was 1188 litre. How much of the solution in the second container was made up of ingredient B?

Correct — A. Both containers hold the same solution, so what carries across is the ratio, not the litres.

First container, A : B = 252 : 441
Divide both by 63 → 4 : 7, so the solution splits into 11 equal parts

Second container: 1,188 ⁄ 11 = 108 litre per part
B = 7 × 108 = 756 litre → option (a)

Check: A = 4 × 108 = 432 litre, and 432 + 756 = 1,188 litre.

Why the others are wrong

• (b)
  760 litre — 760 is not a multiple of 7, and B has to be seven equal parts — 760 ⁄ 7 = 108.57. It would also leave 428 litre of A, and 428 : 760 does not reduce to 4 : 7.
• (c)
  765 litre — 765 ⁄ 7 = 109.28, so it cannot be seven whole parts either. It leaves 423 litre of A, and 423 : 765 is nowhere near 4 : 7.
• (d)
  752 litre — 752 leaves 436 litre of A, and 436 : 752 does not reduce to 4 : 7, the ratio the first container fixes for both.

A solution is defined by its proportions, so two containers of the same solution differ only in scale.

252 : 441 shares the factor 63 — 252 = 4 × 63 and 441 = 7 × 63 — so the ratio is 4 : 7, eleven parts in all.

Any quantity of that solution then divides into eleven equal parts. 1,188 ⁄ 11 = 108, so A takes 432 litre and B takes 756 litre.

You could also scale directly: the second container is 1,188 ⁄ 693 times the first, and 441 × 1,188 ⁄ 693 = 756 litre. Same answer, one fewer reduction.

Key facts

• 252 : 441 reduces to 4 : 7 because both terms share the factor 63.
• The same solution in a different container keeps the ratio, not the quantities.
• 1,188 litre splits into 11 equal parts of 108 litre, so A is 432 litre and B is 756 litre.

Common traps

• Carrying the litres 252 and 441 across instead of the ratio.
• Splitting 1,188 in the ratio 7 : 4 and answering 432 litre.
• Reading 1,188 as the quantity of one ingredient rather than the whole solution.

No directly related past PYQ was found.