Multiple choice

In a 140 litres of mixture of milk and water, percentage of water is only 30%. The milkman gave 20 litres of this mixture to a customer. Then he added equal quantities of pure milk and water to the remaining mixture. As a result the respective ratio of milk and water in the mixture became 2 : 1. What was the quantity of milk added? (in litres)

  1. 12

  2. 16

  3. 18

  4. 8

  5. 10
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A Correct answer
Explanation

Initial: 140L, 30% water (42L), 70% milk (98L). Remove 20L: 140-20=120L remaining. Ratio 7:3 remains, so 84L milk, 36L water. Add x L of each: (84+x)/(36+x) = 2/1. 84+x = 72+2x => x = 12.

AI explanation

Using the method of finding the mixture composition after removal, the 20 litres removed from the 140 litre mixture leaves 120 litres. Since the mixture was originally 30 percent water and 70 percent milk, the remaining 120 litres contains 36 litres of water and 84 litres of milk. The problem states that the milkman adds equal quantities of pure milk and water, let us call this quantity x, making the total milk 84 + x and total water 36 + x. Because the new ratio of milk to water is 2 to 1, the equation is 84 + x = 2 multiplied by (36 + x), which simplifies to 84 + x = 72 + 2x, meaning x equals 12 litres of milk added.

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