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In a mixture of 280 liters, the ratio of the milk and water is 5:2. If the x liters of the mixture is taken out and the x liters of water is added to the resultant mixture, then the ratio of milk to water in the resultant mixture becomes 5:3, find the quantity of the water in the final mixture?

1. 75 liters
2. 90 liters
3. 105 liters
4. 120 liters

Correct answer: 105 liters

Solution

Total=280L, ratio 5:2. Milk=200L, water=80L. Remove x L (5:2 ratio), add x L water. Milk after = 200-5x/7. Water after = 80+5x/7. New ratio: (200-5x/7)/(80+5x/7)=5/3 → 600-15x/7=400+25x/7 → 200=40x/7 → x=35. New water = 80+5×35/7 = 80+25 = 105L.

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