Multiple choice

Two vessels A and B of equal volume contain milk and water in the ratio 3 : 2 and 2 : 1 to their brim respectively. Two litres of the solution from vessel A and three litres of the solution from vessel B are poured into a big empty vessel C. If the solution in C occupied 40% of the capacity of C, what proportion of the volume of vessel C should be the volume of water that shall be added so that the ratio of milk and water in vessel C becomes 1 : 1?

  1. 21/125

  2. 2/25

  3. 4/75

  4. 14/125

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Vessel A: 2L, 3:2 ratio (1.2L milk, 0.8L water). Vessel B: 3L, 2:1 ratio (2L milk, 1L water). Total in C: 3.2L milk, 1.8L water (Total 5L). C is 40% full, so capacity = 5/0.4 = 12.5L. To get 1:1 ratio, we need 3.2L water total. Currently 1.8L, so add 1.4L water. 1.4/12.5 = 14/125.

AI explanation

Vessel A contains milk and water in a 3 : 2 ratio, so taking 2 liters means 1.2 liters of milk and 0.8 liters of water. Vessel B contains a 2 : 1 ratio, so 3 liters yields 2 liters of milk and 1 liter of water. In vessel C, the total is 3.2 liters of milk and 1.8 liters of water, which is 5 liters total, making the capacity of C equal to 5 divided by 0.40, or 12.5 liters. To make the milk and water equal, you must add 1.4 liters of water (3.2 minus 1.8), and the required proportion of vessel C is 1.4 divided by 12.5, which equals 14/125.

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