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 :
The average weight of three men A, B, and C is 84 kg.
$\therefore$ The total weight of A, B, and C = 84 × 3 = 252 kg
Now, D joins the group and the average now becomes 80 kg.
$\therefore$ Weight of D = (80 × 4) – 252 = 68 kg
E's weight is 3 kg more than that of D.
So, E's weight = 68 + 3 = 71 kg
He replaces A.
The average weight of B, C, D, and E becomes 79 kg.
So, the weight of (B + C) = (79 × 4) – (68 + 71) = 177 kg
$\therefore$ Weight of A = 252 – 177 = 75 kg
Hence, the correct answer is 75 kg.
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