The average weight of three friends A, B and C is 46 kg. Another person D joins the group and now the average weight is 45 kg. If another person E whose weight is 6 kg more than D joins the group replacing A, then the average weight of B, C, D and E becomes 47 kg. What is the weight of A (in kg)?
The average weight of three friends A, B and C is 46 kg. Another person D joins the group and now the average weight is 45 kg. If another person E whose weight is 6 kg more than D joins the group replacing A, then the average weight of B, C, D and E becomes 47 kg. What is the weight of A (in kg)? Correct Answer 40 kg
Given:
Average weight of three friends A, B and C is 46 kg
Average weight when D joins the group is 45 kg
Weight of E is 6 kg more than D
Average weight of B, C, D and E = 47 kg
Formula used:
Average = (Sum of all the observations)/(Total number of observations)
Calculation:
According to the question,
Average weight of three friends A, B and C is 46 kg
Total weight of A, B and C
⇒ A + B + C = 46 × 3 = 138 kg
Another person D joins the group and now the average weight is 45 kg
Total weight of A, B, C and D
⇒ A + B + C + D = 45 × 4 = 180 kg ----(i)
⇒ Weight of D = 180 – 138 = 42 kg
Now,
Weight of E is 6 kg more than D
⇒ E = D + 6
⇒ E = 42 + 6 = 48 kg
Now,
Average weight of B, C, D and E is 47 kg
⇒ B + C + D + E = 47 × 4 = 188 kg ----(ii)
From equation (i) and (ii),
⇒ E – A = 188 – 180 = 8 kg
⇒ 48 – A = 8
⇒ A = 40 kg
∴ Weight of A is 40 kg
