Question : 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. A 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. What is the average weight (in kg) of A, D and E? (correct to the nearest integer)
Option 1: 40
Option 2: 35
Option 3: 30
Option 4: 39
Correct Answer: 35
Solution :
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
The sum of weight = average × number of observations
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)
Subtract (1) from (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 [Using equation (3)]
⇒ B + C + 30 + 35 = 236
⇒ B + C = 236 – 65
⇒ B + C = 171 kg---------------------------(4)
Subtract (4) from (1),
(A + B + C) – (B + C) = 210 – 171
⇒ A = 39 kg
The average weight (in kg) of A, D and E $=\frac{39+30+35}{3} = \frac{104}{3}= 34.6 \approx 35$
Hence, the correct answer is 35.
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