The average weight of four boys A, B, C, and D is 75 kg. The fifth boy E is included and the average weight decreases by 4 kg. A is replaced by F. The weight of F is 6 kg more than E. Average weight decreases because of the replacement of A and now the average weight is 72 kg. Find the weight of A. 57 kg 54 kg 56 kg 60 kg
Question
The average weight of four boys A, B, C, and D is 75 kg. The fifth boy E is included and the average weight decreases by 4 kg. A is replaced by F. The weight of F is 6 kg more than E. Average weight decreases because of the replacement of A and now the average weight is 72 kg. Find the weight of A. 57 kg 54 kg 56 kg 60 kg
Solution
To solve this problem, we need to follow these steps:
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The average weight of A, B, C, and D is 75 kg. This means the total weight of these four boys is 75 kg * 4 = 300 kg.
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When E is included, the average weight decreases by 4 kg to 71 kg. This means the total weight of A, B, C, D, and E is 71 kg * 5 = 355 kg. Therefore, the weight of E is 355 kg - 300 kg = 55 kg.
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A is replaced by F, and the average weight decreases to 72 kg. This means the total weight of B, C, D, E, and F is 72 kg * 5 = 360 kg.
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The weight of F is 6 kg more than E. So, the weight of F is 55 kg + 6 kg = 61 kg.
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Now, we can find the weight of A. Before A was replaced, the total weight was 355 kg. After A was replaced by F, the total weight became 360 kg. So, the weight of A is 360 kg - 355 kg + 61 kg = 66 kg.
However, none of the options provided (57 kg, 54 kg, 56 kg, 60 kg) match this result. There might be a mistake in the problem or the options provided.
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