The average weight of the girls in a group is 58 kg. When 5 girls of average weight 60 kg leave the group or 5 girls of average weight 55.5 kg join the group, the average weight of girls in both cases is equal. What is the number of girls, initially, in the group?

Correct option is C

Given:

Average weight of girls initially = 58 kg

5 girls of average 60 kg leave the group or

5 girls of average 55.5 kg join the group

In both cases, the new average is the same.

Find the initial number of girls.

Formula Used:

Total weight = (Number of girls) × (Average weight)

Solution:

Let the initial number of girls be x.

Initial total weight: 58x

For, 5 girls (avg 60 kg) leave

New total weight = 58x - (5 × 60) = 58x - 300

New number of girls = x - 5

New average = $$\frac{58x - 300}{x - 5}$$​​

5 girls (avg 55.5 kg) join

New total weight = 58x + (5 × 55.5) = 58x + 277.5

New number of girls = x + 5

New average = $$\frac{58x + 277.5}{x + 5}$$​​

Since both averages are equal:

​$$\frac{58x - 300}{x - 5} = \frac{58x + 277.5}{x + 5}$$​​

(58x - 300)(x + 5) = (58x + 277.5)(x - 5)

​$$58x^2 - 10x - 1500 = 58x^2 - 12.5x - 1387.5$$​​

2.5x = 112.5

x = 45

Thus, Initial number of girls is 45

Alternate Solution (Exam Trick):