Question

The ratios of number of red pens to the number of blue pens in a shop is 3:7. There are 64 more blue pens than red pens. If the no. of red pens increases by 12, find the new ratio of no. of red pens to the no. of blue pens.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{red}\mathrm{pens}=3\mathrm{x} \\ \mathrm{then}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{blue}\mathrm{pens}=7\mathrm{x} \\ \mathrm{Now},\mathrm{according}\mathrm{to}\mathrm{question}, \\ 3\mathrm{x}+64=7\mathrm{x} \\ \Rightarrow 4\mathrm{x}=64 \\ \Rightarrow \mathrm{x}=16 \\ \mathrm{Now},\mathrm{number}\mathrm{of}\mathrm{red}\mathrm{pens}=3\times 16=48 \\ \mathrm{number}\mathrm{of}\mathrm{blue}\mathrm{pens}=7\times 16=112 \\ \mathrm{Now},\mathrm{when}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{red}\mathrm{pens}\mathrm{is}\mathrm{increased}\mathrm{by}12, \\ \mathrm{number}\mathrm{of}\mathrm{red}\mathrm{pens}=48+12=60 \\ \mathrm{Now}, \\ \frac{\mathrm{number}\mathrm{of}\mathrm{red}\mathrm{pens}}{\mathrm{number}\mathrm{of}\mathrm{blue}\mathrm{pens}}=\frac{60}{112}=\frac{15}{28} \end{gathered}$$