Multiple choice

The average weight of a group of 3 people A, B and C is 70 kg. When D joins this group, the average weight 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)

  1. 39

  2. 35

  3. 30

  4. 40
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B Correct answer
Explanation

Initial: A+B+C = 3 * 70 = 210. A+B+C+D = 4 * 60 = 240, so D = 30. E = D + 5 = 35. New group: B+C+D+E = 4 * 59 = 236. Since B+C = 210 - A, we have (210 - A) + 30 + 35 = 236. 275 - A = 236, so A = 39. Average of A, D, E = (39 + 30 + 35) / 3 = 104 / 3 = 34.66, which is 35 rounded.

AI explanation

From the first average, the sum of weights of A, B, and C is 210 kg. Adding D makes the sum 240 kg, so D weighs 30 kg. E weighs 5 kg more, so E is 35 kg. The new average of B, C, D, and E is 59, meaning their total weight is 236 kg. Since D and E together weigh 65 kg, B and C must weigh 171 kg. Because A, B, and C weigh 210 kg, A weighs 39 kg. The average weight of A, D, and E is (39 + 30 + 35) / 3, which equals 34.67 kg, rounding to 35 kg.

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