Question

Mark the correct alternative in the following question:

The ages of Ravish and Shikha are in the ratio 3 : 8. Six years hence, their ages will be in the ratio 4 : 9. The present age of Ravish is

(a) 18 years (b) 15 years (c) 12 years (d) 21 years

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{present}\mathrm{age}\mathrm{of}\mathrm{Ravish}\mathrm{and}\mathrm{Shikha}\mathrm{be}3x\mathrm{and}8x,\mathrm{respectively}. \\ \mathrm{After}\mathrm{six}\mathrm{years}, \\ \mathrm{Age}\mathrm{of}\mathrm{Ravish}=\left(3x+6\right)\mathrm{years}\mathrm{and} \\ \mathrm{Age}\mathrm{of}\mathrm{Shikha}=\left(8x+6\right)\mathrm{years} \\ \mathrm{Since},\left(3x+6\right):\left(8x+6\right)=4:9 \\ \Rightarrow \frac{\left(3x+6\right)}{\left(8x+6\right)}=\frac{4}{9} \\ \Rightarrow 9\left(3x+6\right)=4\left(8x+6\right) \\ \Rightarrow 27x+54=32x+24 \\ \Rightarrow 27x-32x=24-54 \\ \Rightarrow -5x=-30 \\ \Rightarrow x=\frac{-30}{-5} \\ \Rightarrow x=6 \\ \therefore 3x=3\times 6=18 \end{gathered}$$

So, the present age of Ravish is 18 years.

Hence, the correct alternative is option (a).