A vessel contains a mixture of milk and water in the ratio 4:5. On adding 26 litres of water to the vessel, the ratio of water to milk becomes 4:3. If $K$ litres of milk are added to the initial mixture so that the ratio of milk to water becomes 17:13, find the value of $K$.

Question

Accepted Answer

198 L. Let the initial milk and water be $4x$ and $5x$. After adding 26 L water, $\frac{5x+26}{4x}=\frac{4}{3}$, which gives $15x+78=16x$, so $x=78$. Thus initial milk = 312 L and water = 390 L. If $K$ litres of milk are added, $\frac{312+K}{390}=\frac{17}{13}$, giving $13(312+K)=6630$, so $K=198$ L.

A vessel contains a mixture of milk and water in the ratio 4:5. On adding 26 litres of water to the vessel, the ratio of water to milk becomes 4:3. If \(K\) litres of milk are added to the initial mixture so that the ratio of milk to water becomes 17:13, find the value of \(K\).

Solution

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