Question

Mark the correct alternative in the following question:

The boys and girls in a school are in the ratio 9 : 5. If the number of girls is 320, then the total strength of the school is

(a) 840 (b) 896 (c) 920 (d) 576

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{boys}\mathrm{in}\mathrm{the}\mathrm{school}\mathrm{be}x. \\ \mathrm{Since},\mathrm{the}\mathrm{ratio}\mathrm{of}\mathrm{boys}\mathrm{and}\mathrm{girls}\mathrm{in}\mathrm{the}\mathrm{school}=9:5 \\ \Rightarrow \frac{\mathrm{Number}\mathrm{of}\mathrm{boys}}{\mathrm{Number}\mathrm{of}\mathrm{girls}}=\frac{9}{5} \\ \Rightarrow \frac{x}{320}=\frac{9}{5} \\ \Rightarrow 5x=320\times 9 \\ \Rightarrow x=\frac{320\times 9}{5} \\ \Rightarrow x=64\times 9 \\ \Rightarrow x=576 \\ \therefore \mathrm{The}\mathrm{total}\mathrm{strength}\mathrm{of}\mathrm{the}\mathrm{school}=576+320=896 \end{gathered}$$

Hence, the correct alternative is option (b).