A cricket academy has batters and bowlers in the ratio $3 : 5$. After 9 new batters join, the ratio becomes $3 : 4$. How many batters does the academy have now?

Explanation

1. 01

   Let the batters be 3x and the bowlers 5x. The bowlers do not change.

2. 02

   $\frac{3x + 9}{5x} = \frac{3}{4}$ gives $12x + 36 = 15x$, so $x = 12$.

3. 03

   Batters now = $3 \times 12 + 9 = 45$.