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25 liters are drawn from a vessel full of wine and is then filled with water. This operation is performed one more time. The ratio of the quantity of wine now left in the vessel to that of the water is 36 : 85. How much wine the vessel hold initially?

25 liters are drawn from a vessel full of wine and is then filled with water. This operation is performed one more time. The ratio of the quantity of wine now left in the vessel to that of the water is 36 : 85. How much wine the vessel hold initially? Correct Answer 55 liters

Given:

25 liters are drawn from a vessel full of wine and is then filled with water. This operation is performed one more time.

The ratio of the quantity of wine now left in the vessel to that of the water is 36 : 85. 

Concept used:

Wine left = Initial amount of wine × n, where n is the number of times the wine is replaced

Calculation:

Let the initial quantity of wine be y litres

Amount of wine left = y × (1 - 25/y)2 

Ratio of wine left to initial quantity of wine = y × (1 - 25/y)2/y = (1 - 25/y)2  

⇒ 36/(36 + 85) = (1 – 25/y)2 

⇒ 36/121 = (6/11)2 = (1 – 25/y)2 

⇒ 6/11 = 1 – 25/y

On Solving, y = 55 liters

∴ 55 litres

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