The average weight of a certain number of students in a group was 72 kg. If 11 students, with an average weight of 76 kg each, leave the group, and 5 students, each with an average weight of 79 kg, join the group, the average weight of the students in the group decreases by 0.6 kg. The number of students initially in the group was:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e 21.
New average = 72 − 0.6 = 71.4 kg
Let the initial number of students = x
Total weight = 72x
Total weight lost (11 students leave) = 11 × 76 = 836 kg
Total weight gained (5 students join) = 5 × 79 = 395 kg
New total weight = 72x − 836 + 395 = 72x − 441
New number of students = x − 11 + 5 = x − 6
New average = (72x − 441)/(x − 6) = 71.4
⇒ 72x − 441 = 71.4(x − 6)
⇒ 72x − 441 = 71.4x − 428.4
⇒ 72x − 71.4x = 441 − 428.4 ⇒ 0.6x = 12.6 ⇒ x = 12.6/0.6 = 21