Expert: Pawan Musale - 1/29/2011

Question
On the first day of school, the % of boys in a class is 60%. During the year, six girls moved away, and are replaced by six boys; this makes the class roster 75% boys. Find the number of boys and girls in the class on the first day of school.

Answer
Charles,

Say, total students in class = x
On first day,
boys = 60% of total students (x)
Hence, boys (say b) = 0.6x
Hence, girls (say g) = x - 0.6x = 0.4x
Now, during the year 6 boys were added.
Hence total number of boys = 0.6x + 6 ----------------------------- (1)
After this addition, total boys count is 75% of total class.
Hence total number of boys = 0.75x ----------------------------- (2)
Equations (1) and (2) above give us total number of boys. Hence we will equate these two equations
0.6x+6 = 0.75x
On solving,
6 = 0.75x-0.6x
6 = 0.15x
x = 40 ----------------------- (3)
Hence, total students in class (x) = 40
Now inititally boys were 0.6x (see beginning of this solution)
Hence, boys = 0.6 * 40 = 24
And girls = 0.4x = 0.4 * 40 = 16

I hope this is clear.

Kindly let me know if you have any questions.

All the best :)

Regards,
Pawan