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Two vessels a and b of the equal volume contain milk and water in the ratio 3 ∶ 2 and 2 ∶ 1 respectively. Two liters of the solution from the vessel a and three liters of the solution from vessel b are poured in 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?

Two vessels a and b of the equal volume contain milk and water in the ratio 3 ∶ 2 and 2 ∶ 1 respectively. Two liters of the solution from the vessel a and three liters of the solution from vessel b are poured in 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? Correct Answer 14/125

Correct answer is option 4 i.e 14/125

In 2 litres of vessel a solution, milk = 2 × 3/5 = 1.2 litres

In 2 litres of vessel a solution, water = 2 × 2/5 = 0.8 litres

In 3 litres of vessel b solution, milk = 3 × 2/3 = 2 litres

In 3 litres of vessel b solution, water = 3 × 1/3 = 1 litre

In vessel c,

Milk = 1.2 + 2 = 3.2 litres

Water = 0.8 + 1 = 1.8 litres

Total = 3.2 + 1.8 = 5 litres

40% of c = 5 litres

100% of c = 5/40 × 10 = 12.5 litres

The required proportion = (3.2 – 1.8)/12.5 = 14/125

Hence, the correct answer is 14/125.

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