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The initial quantities of milk and water in a vessel are 30x litres and 10x litres respectively. After 80 litres of the mixture is taken out, the quantities of milk and water removed are in the ratio 3:1. If 80 litres of water is then added and the resulting ratio of milk to water becomes 4:1, find the original quantity of the mixture in the vessel.

1. 120
2. 140
3. 160
4. 180

Correct answer: 160

Solution

From the 3:1 removal ratio, 60 litres milk and 20 litres water are removed. So remaining milk = 30x - 60 and remaining water = 10x - 20. After adding 80 litres water, water becomes 10x + 60, and the final ratio milk:water = 4:1 gives 30x - 60 = 4(10x + 60). Solving gives x = 4, so the original mixture = 30x + 10x = 160 litres.

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