A milk man mixed 1 : 4 solution of milk and water with another 1 : 2 solution…

2025

A milk man mixed 1 : 4 solution of milk and water with another 1 : 2 solution of milk and water in the volume of ratio 3 : 2. If the profit earned by selling the first solution was 20% and the mixture was sold at the same price, what is the profit or loss percentage? You have to assume that water comes free of cost.

  1. A.

    5.26% profit

  2. B.

    5.25% loss

  3. C.

    6.25% loss

  4. D.

    None of these

Attempted by 13 students.

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Correct answer: B

Solution: Let the cost of 1 unit of pure milk be 1.

  • First solution (milk:water = 1:4): milk fraction = 1/(1+4) = 1/5. Cost price (CP) per litre = 1/5. It is sold at 20% profit, so selling price (SP) per litre = (1/5) × 1.20 = 6/25.

  • Second solution (milk:water = 1:2): milk fraction = 1/(1+2) = 1/3.

  • Mix in volumes 3:2. Overall milk fraction = (3×1/5 + 2×1/3)/(3+2) = (3/5 + 2/3)/5 = 19/75. So CP per litre of the mixture = 19/75.

  • The mixture is sold at the same SP as the first solution: SP = 6/25. Compare CP and SP: CP − SP = 19/75 − 6/25 = 19/75 − 18/75 = 1/75 (loss per litre).

  • Loss percentage = (loss per litre)/(CP per litre) × 100 = (1/75)/(19/75) × 100 = (1/19) × 100 = 100/19% ≈ 5.263% loss.

  • Conclusion: The transaction yields a loss of 100/19% (about 5.263%). The given option '5.25% loss' is a close rounded value but the exact loss is 100/19% ≈ 5.263%.

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