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The manager at a dairy farm has five similar cans of 50 litres capacity - A, B, C, D and E - full of mixtures of milk and water. The ratio of milk and water in each can is different. It is known that the cost price of pure milk is Rs. 25 and water is free of cost. When he sells the entire contents of can E at Rs. 1,250, the manager earns a profit of 25%. Can C contains 20 litres more of milk than water. If the manager sells the mixture in can B at the cost price of milk, he earns a profit of 100%. The cost price of the mixture in can D is Rs. 800. The water content in can A is as much less than can B as it is more than can C.Q 115.   If equal quantities of mixtures from cans A and B are mixed in a new vessel, then what is the percentage of milk in the new mixture?a)  40%b)  50%c)  55%d)  48%

Question

The manager at a dairy farm has five similar cans of 50 litres capacity - A, B, C, D and E - full of mixtures of milk and water. The ratio of milk and water in each can is different. It is known that the cost price of pure milk is Rs. 25 and water is free of cost. When he sells the entire contents of can E at Rs. 1,250, the manager earns a profit of 25%. Can C contains 20 litres more of milk than water. If the manager sells the mixture in can B at the cost price of milk, he earns a profit of 100%. The cost price of the mixture in can D is Rs. 800. The water content in can A is as much less than can B as it is more than can C.Q 115.   If equal quantities of mixtures from cans A and B are mixed in a new vessel, then what is the percentage of milk in the new mixture?a)  40%b)  50%c)  55%d)  48%

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Solution

To solve this problem, we need to first understand the information given for each can.

  1. Can E: The entire contents of can E are sold at Rs. 1,250, which is a 25% profit. This means the cost price of the mixture in can E is Rs. 1,250 / 1.25 = Rs. 1,000. Since the cost of water is free, the cost of the milk in can E is Rs. 1,000. As the cost of 1 litre of milk is Rs. 25, can E contains 1,000 / 25 = 40 litres of milk and 10 litres of water.

  2. Can C: Can C contains 20 litres more milk than water. As the total capacity of the can is 50 litres, it contains 35 litres of milk and 15 litres of water.

  3. Can B: If the manager sells the mixture in can B at the cost price of milk, he earns a profit of 100%. This means the mixture in can B contains 50% milk and 50% water. So, can B contains 25 litres of milk and 25 litres of water.

  4. Can A: The water content in can A is as much less than can B as it is more than can C. So, the water content in can A is 20 litres and the milk content is 30 litres.

Now, if equal quantities of mixtures from cans A and B are mixed in a new vessel, the total quantity of milk is 30 litres (from A) + 25 litres (from B) = 55 litres. The total quantity of the mixture is 50 litres (from A) + 50 litres (from B) = 100 litres.

Therefore, the percentage of milk in the new mixture is (55 / 100) * 100 = 55%.

So, the answer is c) 55%.

This problem has been solved

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