Playing Children

      A group of boys and girls are playing. 15 boys leave.

        There remain two girls for each boy. Then 45 girls leave. There remain five boys for each girl. How many boys were in the original group?

Answer: 40 boys.

Let G represent the number of girls in the original group and B the number of boys in the original group. Then we have:

G / B -15 = 2/1 and G – 45 / B – 15 = 1/5

Then G = 2 (B- 15)

             5(G -45) = (B – 15)

Solving the simultaneous equations above we get:

B = 40 and G = 50