A vessel contains a mixture of orange juice and water in the ratio 3:5. How many litres should be replaced with water so that the ratio becomes 2:5, given the total mix is 168 L?
40 L
Orange juice in 168 L = \(\frac{3}{8}\) × 168 = 63 L; water = 105 L.
If x L of the mixture is removed and replaced with water, the juice removed is \(\frac{3x}{8}\) L, and the total stays 168 L.
For the ratio 2:5, juice must be \(\frac{2}{7}\) × 168 = 48 L.
So 63 − \(\frac{3x}{8}\) = 48, giving \(\frac{3x}{8}\) = 15 and x = 40.
Hence, the answer is 40 L.
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