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A milkman has 48 litres of mixture of milk and water in the ratio 5 : 1, respectively. He withdraws some amount of the mixture from the vessel and replaces it with milk. The ratio of the mixture of milk and water now becomes 7 : 1. What amount of the mixture is withdrawn?
  • a)
    10 litres
  • b)
    15 litres
  • c)
    16 litres
  • d)
    None of these
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A milkman has 48 litres of mixture of milk and water in the ratio 5 : ...
Given:
- The original mixture contains 48 litres of milk and water in the ratio of 5:1.
- The milkman withdraws some amount of the mixture and replaces it with milk.
- The new ratio of the mixture becomes 7:1.

Let's assume that the milkman withdraws 'x' litres of the mixture.

Determining the amount of milk and water in the original mixture:
- The ratio of milk to water in the original mixture is 5:1, which means that out of every 5 parts, 5/6 parts are milk and 1/6 part is water.
- Let's assume that there are 5a litres of milk and a litres of water in the original mixture.

After withdrawing 'x' litres of the mixture:
- The amount of milk left in the mixture is (5a - 5x) litres.
- The amount of water left in the mixture is (a - x) litres.

Adding milk to the mixture:
- The milkman adds 'x' litres of milk to the mixture.
- The new amount of milk in the mixture is (5a - 5x + x) = (5a - 4x) litres.

Given that the new ratio of the mixture is 7:1, we can write the equation:
(5a - 4x) / (a - x) = 7/1

Cross-multiplying, we get:
7(a - x) = (5a - 4x)

Expanding and simplifying, we get:
7a - 7x = 5a - 4x

Bringing all the 'x' terms on one side and all the 'a' terms on the other side, we get:
7a - 5a = 7x - 4x
2a = 3x

Simplifying further, we get:
x = (2a/3)

Since x represents the amount of mixture withdrawn, it should be an integer. However, 'a' can take any positive value, and 2a/3 will not always be an integer.

Hence, it is not possible to determine the exact amount of mixture withdrawn. Therefore, the correct answer is option 'D' - None of these.
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