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

Total student in the class = 154