Question
A container has milk and water in the ratio 2:3. 20
litres of the mixture is removed and replaced by milk. The operation is repeated once again. If the final ratio of water to milk becomes 48:77, find the total capacity of the container (assume it stays full).Solution
ATQ, Let the total capacity be P litres. Initially, fraction of water = 3/5. Final water fraction = (3/5) × ((P - 20)/P)² Given final water:milk = 48:77 ⇒ water fraction = 48/125. So, 48/125 = (3/5) × ((P - 20)/P)² ⇒ 16/25 = ((P - 20)/P)² ⇒ 4/5 = (P - 20)/P ⇒ 4P = 5(P - 20) ⇒ P = 100 Therefore, capacity of the container = 100 litres.
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