A vessel contains 56 litres of mixture of milk and water in the ratio 5 : 2. How much water should be mixed with it so that the milk to water ratio becomes 4 : 5?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 34 litres
\( \displaystyle \text{Milk} = \frac{5}{7}\times 56 = 40 \text{ litres}, \quad \text{Water} = 56-40 = 16 \text{ litres} \)
Adding water does not change the milk. Let x litres of water be added:
\( \displaystyle \frac{40}{16+x} = \frac{4}{5} \)
\(200 = 64+4x\)
\(4x = 136\)
\(x = 34\)
So 34 litres of water must be added (then milk : water = 40 : 50 = 4 : 5).