A vessel contains 26 litres of milk. 13 litres of milk was taken out from this vessel and replaced with water. This process was repeated once more. How much milk is now in the vessel?
6.5 litres
When x litres of liquid is drawn off from a vessel of V litres and replaced with water, and this is done n times, the quantity of original liquid remaining is V(1 − x/V)ⁿ.
Here V = 26, x = 13 and n = 2, so milk remaining = 26 × (1 − 13/26)² = 26 × (1/2)².
= 26 × 1/4 = 26/4 = 6.5 litres. Hence, the correct answer is 6.5 litres.
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Important Questions from Mixture Problems
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5 litres are drawn from a cask full of wine and is then filled with water. This operation is performed once more. The ratio of the quantity of wine now left in cask to that of the water is 16:9. How much wine the cask hold originally? (In litres)
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