The average weight of a group of 3 people A, B and C is 70 kg. When D joins this group, the average becomes 60 kg, One man E, whose weight is 5 kg more than that of D, replaces A and the average weight of B, C, D, and E now becomes 59 kg. A's weight (in kg) is:
The average weight of a group of 3 people A, B and C is 70 kg. When D joins this group, the average becomes 60 kg, One man E, whose weight is 5 kg more than that of D, replaces A and the average weight of B, C, D, and E now becomes 59 kg. A's weight (in kg) is: Correct Answer 39
Given:
Average weight of A, B, and C = 70 kg
Average weight of A, B, C, and D = 60 kg
Weight of E = Weight of D + 5 kg
Average weight of B, C, D and E = 59 kg
Concept used:
Sum of weight = Average × Number of observation
Calculation:
A + B + C = 70 × 3
⇒ A + B + C = 210 kg .............(1)
A + B + C + D = 60 × 4
⇒ A + B + C + D = 240 kg .............(2)
B + C + D + E = 59 × 4
⇒ B + C + D + E = 236 kg ............ (3)
Subtracrt (1) in (2),
(A + B + C + D) – (A + B + C) = 240 – 210
⇒ D = 30 kg
Weight of E = Weight of D + 5 kg
⇒ E = 30 + 5
⇒ E = 35 kg
B + C + D + E = 236
⇒ B + C + 30 + 35 = 236
⇒ B + C = 236 – 65
⇒ B + C = 171 kg ------------(4)
Subtract (4) in (1)
(A + B + C) – (B + C) = 210 – 171
⇒ A = 39 kg
∴ The weight of A is 39 kg.
