Multiple choice

In an experiment, a container with 80 litres of a liquid mixture has two solutions X and Y in the ratio of 3 : 5. After introducing an additional amount of solution Y into the container, the revised ratio of the two solutions becomes 3 : 7. On the removal of one-fifth of this liquid mixture, what quantity of solution X needs to be added to the remaining solution to obtain a new ratio of X and Y as 5 : 8?

  1. 9 litres

  2. 10 litres

  3. 11 litres

  4. 13 litres

  5. 15 litres
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Initial: 80L, X:Y = 3:5 (30L X, 50L Y). After adding Y, ratio 3:7. Since X is 30, Y must be 70. Added 20L Y. Total 100L. Remove 1/5 (20L), remaining 80L (30:70 ratio, 24L X, 56L Y). Target 5:8 ratio. (24+k)/56 = 5/8 => 8(24+k) = 280 => 192 + 8k = 280 => 8k = 88 => k = 11.

AI explanation

Initially, X is (3 / 8) * 80, or 30 litres, and Y is 50 litres; adding Y to make the ratio 3:7 means X remains 30 litres while Y becomes 70 litres, for a new total of 100 litres. Removing one-fifth of this mixture leaves 80 litres, reducing X to 24 litres and Y to 56 litres. To get an X to Y ratio of 5:8, the required amount of X is (5 / 8) * 56, or 35 litres, so you must add 35 minus 24, which is 11 litres of solution X.

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