Multiple choice

A can contains a mixture of two liquids A and B in the ratio of 3 : 2. When 5 litres of the mixture is drawn and replaced with liquid B, the ratio of A to B becomes 1 : 1. What quantity of liquid A was there in the can initially?

  1. 25 litres

  2. 18 litres

  3. 12 litres

  4. 10 litres
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial ratio A:B = 3:2. Let A = 3x, B = 2x. Total = 5x. Draw 5L: A removed = 3/5 * 5 = 3, B removed = 2/5 * 5 = 2. Remaining: A = 3x - 3, B = 2x - 2 + 5 = 2x + 3. Ratio 1:1 implies 3x - 3 = 2x + 3, so x = 6. Initial A = 3 * 6 = 18.

AI explanation

Using the replacement formula, Final Amount equals Initial Amount multiplied by the quantity left in fraction raised to the number of replacements. Setting the initial amount of A as 3x and B as 2x, we get 3x multiplied by (1 minus 5 divided by 5x) all squared equals 1x. Solving 1 minus (1 divided by x) equals the square root of (1 divided by 3) gives x as 6. The initial quantity of liquid A is 3x, which is 18 litres.

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