Question

Mark the correct alternative in the following question:

What must be added to each term of the ratio 9 : 16 to make the ratio 2 : 3?

(a) 5 (b) 3 (c) 4 (d) 6

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{number}\mathrm{that}\mathrm{must}\mathrm{be}\mathrm{added}\mathrm{to}\mathrm{each}\mathrm{term}\mathrm{of}\mathrm{the}\mathrm{ratio}9:16\mathrm{be}x.\mathrm{Then}, \\ \left(9+x\right):\left(16+x\right)=2:3 \\ \Rightarrow \frac{\left(9+x\right)}{\left(16+x\right)}=\frac{2}{3} \\ \Rightarrow 3\left(9+x\right)=2\left(16+x\right) \\ \Rightarrow 27+3x=32+2x \\ \Rightarrow 3x-2x=32-27 \\ \therefore x=5 \end{gathered}$$

So, 5 must be added to each term of the ratio 9 : 16 to make the ratio 2 : 3.

Hence, the correct alternative is option (a).