Multiple choice

A cane contains a mixture of two liquids, 'A' and 'B' in the ratio 7 : 5. When 9 liters of mixture are drawn off and the cane is filled with 'B', the ratio of 'A' and 'B' becomes 7 : 9 liters. How many liters of Liquid 'A' was initially contained by the cane?

  1. 15.25

  2. 18

  3. 21

  4. 17.5

  5. 16.75
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the initial quantity be V litres. After removing 9 litres, the amount of A is 7(V - 9)/12, and the final ratio makes it 7V/16. Equating these gives V = 36 litres, so the initial amount of A is 7/12 × 36 = 21 litres.

AI explanation

In the initial mixture of 12 total parts, liquid A constitutes 7/12 of the total volume. When 9 liters are drawn off, the remaining amount of liquid A is Initial Volume multiplied by (1 - 9/Initial Volume) multiplied by (7/12). Liquid B is then added to fill the cane, making its new proportion 7/16 of the total volume, meaning the new proportion of A is also 7/16. Equating the proportions gives (1 - 9/V) multiplied by (7/12) equals 7/16, which simplifies to 1 - 9/V = 3/4, yielding an initial volume V of 36 liters. The initial amount of liquid A is therefore 7/12 of 36, which is 21 liters.

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