Question

In a picnic there are boys and girls. Fifteen girls leave, then the boys and girls are left in the ratio of $2:1.$ Later $45$ boys leave and the ratio changes to $1:5.$ The number of girls in the beginning was $8p$ then $p$ is

Answer 1

let the number of girls in beginning be $8p$

and the number of boys be $q$

now, $\frac{2}{1}=\frac{q}{8p-15}....................\left(1\right)\frac{1}{5}=\frac{q-45}{8p-15}.................\left(2\right)$

Dividing (1) by (2)

$10=\frac{q}{q-45}\Rightarrow 10q-450=q\Rightarrow 9q=450\Rightarrow q=50$

So, $\frac{2}{1}=\frac{50}{8p-15}\Rightarrow 8p-15=25\Rightarrow 8p=40\Rightarrow p=5$