Multiple choice

A milkman is selling milk for Rs. 25 per litre at no profit or loss. Determine the ratio in which he should mix water with milk so that on selling it for Rs. 20 per litre, he can earn a profit of 25%.

  1. Milk : Water = 12 : 5

  2. Milk : Water = 16 : 9

  3. Milk : Water = 13 : 7

  4. Milk : Water = 3 : 2

  5. Milk : Water = 1 : 2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Selling price = 20. Profit = 25%. Cost price = 20 / 1.25 = 16. The milkman sells pure milk at 25, but the mixture is effectively costed at 16. Using the allegation rule: (25-16) / (16-0) = 9/16. Ratio of water to milk is 9:16, so Milk:Water = 16:9.

AI explanation

Using the method of alligation on the cost prices, the pure milk costs Rs. 25 per litre, and water costs Rs. 0. To achieve a 25% profit while selling the mixture at Rs. 20 per litre, the required cost price is 20 divided by 1.25, which equals Rs. 16. The ratio of milk to water is proportional to the differences between their individual costs and the mean cost, calculated as (16 minus 0) to (25 minus 16). This gives a ratio of 16 to 9, resulting in Milk : Water = 16 : 9.

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