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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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. 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:
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