There are five students whose average weight is 62 kgs. Then, four new students join the group whose weights are (a + 2), (a – 2), (a + 5) and 2a kgs more than the original average of the group. If the average weight of the group is now 67 kgs, find the value of a.
Explanation:
Total weight of 5 students = 5 × 62 = 310 kgs
Total weight of 4 new students = (62 + a + 2) + (62 + a - 2) + (62 + a + 5) + (62 + 2a) = 62 × 4 + 5a + 5
Average weight of all the nine students = (5 × 62 + 62 × 4 + 5a + 5)/9 = 67
⇒ 9 × 62 + 5a + 5 = 67 × 9
⇒ a = 8
Alternately, Because of these 4 new students, the average of now 9 students increases by 5.
∴ Extra weight of these 4 students = 9 × 5 = 45
⇒ (a + 2) + (a - 2) + (a + 5) + 2a = 45
⇒ 5a = 40
Hence, option (a).
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