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 3 kg more than D replaces A then the average of B C D and E become 79 kg . What is the weight of A ?

• A. 70
• B. 72
• C. 75
• D. 80

Answer 1

Answer:

C. 75

1. Calculate the Total Weight of the Initial Group (A, B, C):

   • Given that the average weight of A, B, and C is 84 Kg, and there are 3 men.

   • Using the formula: Sum = Average × Number

   • Total weight of A + B + C = 84 Kg × 3 = 252 Kg. (Equation 1)

2. Determine the Weight of Man D:

   • When D joins, the group (A, B, C, D) has 4 men, and their average weight becomes 80 Kg.

   • Total weight of A + B + C + D = 80 Kg × 4 = 320 Kg. (Equation 2)

   • Substitute the sum of (A + B + C) from Equation 1 into Equation 2:

   • 252 Kg + D = 320 Kg

   • Weight of D = 320 Kg - 252 Kg = 68 Kg.

3. Calculate the Weight of Man E:

   • It is stated that E's weight is 3 Kg more than D's weight.

   • Weight of E = Weight of D + 3 Kg

   • Weight of E = 68 Kg + 3 Kg = 71 Kg.

4. Find the Total Weight of the Group (B, C, D, E):

   • When E replaces A, the new group consists of B, C, D, and E. There are still 4 men.

   • Their average weight is given as 79 Kg.

   • Total weight of B + C + D + E = 79 Kg × 4 = 316 Kg. (Equation 3)

5. Isolate the Sum of Weights for B and C:

   • Substitute the known weights of D and E into Equation 3:

   • B + C + 68 Kg + 71 Kg = 316 Kg

   • B + C + 139 Kg = 316 Kg

   • Sum of B + C = 316 Kg - 139 Kg = 177 Kg. (Equation 4)

6. Calculate the Weight of Man A:

   • Recall Equation 1: A + B + C = 252 Kg.

   • Now substitute the sum of (B + C) from Equation 4 into Equation 1:

   • A + 177 Kg = 252 Kg

   • Weight of A = 252 Kg - 177 Kg = 75 Kg.