Question

Tick (✓) the correct answer:
Number of boys and girls in a class are in the ratio 7 : 5. The number of boys is 8 more than the number of girls. The total class strength is
(a) 56
(b) 52
(c) 48
(d) 36

Answer 1

(c) 48

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{boys}\mathrm{in}\mathrm{the}\mathrm{class}\mathrm{be}\mathrm{x}. \\ \mathrm{Then},\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{girls}\mathrm{will}\mathrm{be}(\mathrm{x}-8). \\ \mathrm{The}\mathrm{equation}\mathrm{becomes}: \\ \frac{x}{x-8}=\frac{7}{5} \\ \Rightarrow 5x=7x-56 \\ \Rightarrow 5x-7x=-56 \\ \Rightarrow -2x=-56 \\ \Rightarrow x=\frac{-56}{-2}=28 \\ \mathrm{Therefore},\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{boys}\mathrm{is}28. \\ \mathrm{Number}\mathrm{of}\mathrm{girls}=(\mathrm{x}-8)=28-8=20 \\ \mathrm{Total}\mathrm{strength}\mathrm{of}\mathrm{the}\mathrm{class}=28+20=48 \end{gathered}$$