Question

The average weight of 3 men A, B, and C is 84 kgs. Another man D joins the group and the average now becomes 80 kgs. If another man E, whose weight is 3 kgs more than that of D, replaces A, then the average weight of B, C, D, and E becomes 79 kgs. What is the weight of A?

• A. 70
• B. 72
• C. 80
• D. 75

Hint:

In such problems, break down the information into manageable parts, use equations to represent the given conditions, and solve step by step.

Answer 1

The Correct Option is D

Let the weights of A, B, and C be \( A, B, C \) respectively.
- The average weight of A, B, and C is 84 kg, so: \[ \frac{A + B + C}{3} = 84 \implies A + B + C = 252 \quad \text{(Equation 1)} \] - After D joins the group, the average becomes 80 kg, so: \[ \frac{A + B + C + D}{4} = 80 \implies A + B + C + D = 320 \quad \text{(Equation 2)} \] - Now, E replaces A and the average of B, C, D, and E becomes 79 kg, so: \[ \frac{B + C + D + E}{4} = 79 \implies B + C + D + E = 316 \quad \text{(Equation 3)} \] - We are told that the weight of E is 3 kg more than that of D, so \( E = D + 3 \). Substituting this into Equation 3: \[ B + C + D + (D + 3) = 316 \implies B + C + 2D + 3 = 316 \implies B + C + 2D = 313 \quad \text{(Equation 4)} \] - Now, subtract Equation 1 from Equation 2: \[ (A + B + C + D) - (A + B + C) = 320 - 252 \implies D = 68 \] - Substituting \( D = 68 \) into Equation 4: \[ B + C + 2(68) = 313 \implies B + C + 136 = 313 \implies B + C = 177 \] - Finally, substitute \( B + C = 177 \) into Equation 1: \[ A + 177 = 252 \implies A = 252 - 177 = 75 \] Thus, the weight of A is 75 kg.