Average Weight of A, B, and C
The average weight of individuals A, B, and C is given as 72 kg.
- Therefore, the total weight of A, B, and C can be calculated as follows:
- Total weight (A + B + C) = Average weight × Number of individuals
- Total weight (A + B + C) = 72 kg × 3 = 216 kg
Inclusion of D
When individual D joins A, B, and C, the new average weight becomes 68 kg.
- The total number of individuals now is 4 (A, B, C, D).
- The new total weight (A + B + C + D) can be calculated:
- Total weight (A + B + C + D) = Average weight × Number of individuals
- Total weight (A + B + C + D) = 68 kg × 4 = 272 kg
Finding the Weight of D
To find the weight of D, we subtract the total weight of A, B, and C from the total weight of A, B, C, and D.
- Weight of D = Total weight (A + B + C + D) - Total weight (A + B + C)
- Weight of D = 272 kg - 216 kg = 56 kg
Inclusion of E
When E joins A, B, C, and D, the average weight of all five becomes 70 kg.
- The total number of individuals is now 5 (A, B, C, D, E).
- The new total weight (A + B + C + D + E) is:
- Total weight (A + B + C + D + E) = Average weight × Number of individuals
- Total weight (A + B + C + D + E) = 70 kg × 5 = 350 kg
Calculating the Weight of E
Now, we can find the weight of E by subtracting the total weight of A, B, C, and D from the total weight of A, B, C, D, and E.
- Weight of E = Total weight (A + B + C + D + E) - Total weight (A + B + C + D)
- Weight of E = 350 kg - 272 kg = 78 kg
Thus, the weight of E is 78 kg.
Correct answer is option 'A'.