Question

Present age of father is $42\mathrm{years}$ and that of his son is $14\mathrm{years}$. Find the ratio of age of father after $10\mathrm{years}$ to the age of son after $10\mathrm{years}$.

Answer 1

We have,

Present age of father$=42\mathrm{years}$

Age of father after $10\mathrm{years}$$=\mathrm{Present}\mathrm{age}\mathrm{of}\mathrm{father}+10$

$$\begin{gathered} =42+10 \\ =52\mathrm{years} \end{gathered}$$

Present age of son$=14\mathrm{years}$

Age of son after $10\mathrm{years}$$=\mathrm{Present}\mathrm{age}\mathrm{of}\mathrm{son}+10$

$$\begin{gathered} =14+10 \\ =24\mathrm{years} \end{gathered}$$

$\begin{array}{rcl}\therefore \mathrm{Ratio}\mathrm{of}\mathrm{age}\mathrm{of}\mathrm{father}\mathrm{after}10\mathrm{years}\mathrm{to}\mathrm{the}\mathrm{age}\mathrm{of}\mathrm{son}\mathrm{after}10\mathrm{years}& =& \frac{\mathrm{Age}\mathrm{of}\mathrm{father}\mathrm{after}10\mathrm{years}}{\mathrm{Age}\mathrm{of}\mathrm{son}\mathrm{after}10\mathrm{years}}\\ & =& \frac{52}{24}\\ & =& \frac{52÷4}{24÷4}\\ & =& \frac{13}{6}\\ & =& 13:6\end{array}$

Hence, required ratio is $13:6$