Question

in class X of a school, the ratio of the number of boys to that of the girls is4:3. If there were 20 more boys and 12 less girls, then the ratio would have been2:1. How many students were there in the class?

Answer 1

ratio of boys to girls = 4:3

let

x= total number of student

$\begin{gathered} n\text{umber of boys = }\frac{4}{7}x \\ n\text{umber of girls =}\frac{3}{7}x \\ \text{If there are 20 more boys and 12 less girls} \\ \frac{2}{3}\times(x+8)=\text{boys} \\ \frac{1}{3}\times(x+8)=\text{girls} \\ \text{boys}=\frac{2}{3}x+\frac{16}{3} \\ \text{girls}=\frac{1}{3}x+\frac{8}{3} \\ \\ \frac{4}{7}x+20=\frac{2}{3}x+\frac{16}{3} \\ \frac{4}{7}x-\frac{2}{3}x=\frac{16}{3}-20 \\ \frac{12x-14x}{21}=\frac{16-60}{3} \\ \frac{-2x}{21}=\frac{-44}{3} \\ -6x=-924 \\ x=\frac{-924}{-6} \\ x=154 \end{gathered}$

Total student in the class = 154