Question : The average weight of three men, A, B and C is 84 kg. Another man, D, joins the group and the average now becomes 80 kg. If another man, E, whose weight is 3 kg more than that of D, replaces A, then the average weight of B, C, D and E becomes 79 kg. Then the weight of A is:
Option 1: 72 kg
Option 2: 74 kg
Option 3: 75 kg
Option 4: 76 kg
Correct Answer: 75 kg
Solution :
Given: The average weight of three men, A, B, and C, is 84 kg. Another man, D, joins the group and the average now becomes 80 kg. If another man, E, whose weight is 3 kg more than that of D, replaces A, then the average weight of B, C, D, and E becomes 79 kg.
Total weight of A + B + C = (84 × 3) = 252 kg
Total weight of A + B + C + D = (80 × 4) = 320 kg
So, the weight of D = (320 – 252) = 68 kg
Now weight of E = (68 + 3) = 71 kg
Total weight of B + C + D + E = (79 × 4) = 316 kg
So, the total weight of B + C = (316 – 68 – 71) = 177 kg
$\therefore$ The weight of A = (252 – 177) = 75 kg
Hence, the correct answer is 75 kg.
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