Question

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:

• A. 21
• B. 25
• C. 17
• D. 19

Answer 1

Answer:

A. 21

Let the initial number of students be (n).

Initial average weight = 72 kg

So total initial weight:

72n

11 students leave with average weight 76 kg:

Weight removed:

$11 \times 76 = 836$

5 students join with average weight 79 kg:

Weight added:

$5 \times 79 = 395$
New average decreases by 0.6 kg:

$72 - 0.6 = 71.4$
New number of students:

n - 11 + 5 = n - 6

Equation:

$72n-836+395=71.4(n-6)$

$72n - 441 = 71.4n - 428.4$
$72n - 71.4n = 441 - 428.4$
$0.6n = 12.6$

$n = \frac{12.6}{0.6} = 21$

Initial number of students = 21