Multiple choice

A can contains a mixture of two liquids A and B in the ratio 7 : 5. When 9 litres of mixture are drawn off and same quantity of B is poured into can , the ratio of A and B becomes 7 : 9 ,litres of liquid A contained by the can initially was

  1. 7

  2. 10

  3. 17

  4. 21
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the initial quantities of liquids A and B be 7x and 5x. When 9 litres of the mixture are removed and replaced with 9 litres of B, the new ratio of A to B becomes (7x - 9 * 7/12) / (5x - 9 * 5/12 + 9) = 7/9, which simplifies to x = 3. Thus, the initial quantity of liquid A was 7 * 3 = 21 litres.

AI explanation

Since 9 litres of the mixture are drawn off, the amount of liquid A removed is 7/12 of 9, which is 21/4 litres. The final ratio of A to B is 7 to 9, meaning the final amount of liquid A is 7/16 of the total volume. Since no liquid A was added back, the remaining amount of liquid A after the removal is 21/4 litres, which equals 7/16 of the total final volume, making the total final volume equal to 12 litres. This means the total initial volume was also 12 litres plus the 9 litres removed, totaling 21 litres, so the initial amount of liquid A was 7/12 of 21, giving 21 litres.

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