Question

Present age of father is $42$ years and that of his son is $14$ years. Find the ratio of (a) Present age of father to the present age of son (b) Age of the father to the age of son, when son was $12$ years old. (c) Age of father after $10$ years to the age of son after $10$ years. (d) Age of father to the age of son when father was $30$ years old.

Answer 1

Step 1. Determine the ratio of present age of father to the present age of son.

Present age of father is $42\mathrm{years}$
Present age of son is $14\mathrm{year}s$

$\begin{array}{rcl}\mathrm{Ratio}& =& \frac{\mathrm{Present}\mathrm{age}\mathrm{of}\mathrm{father}}{\mathrm{Present}\mathrm{age}\mathrm{of}\mathrm{son}}\\ & =& \frac{42}{14}\\ & =& \frac{3}{1}\\ & =& 3:1\end{array}$

Hence, the ratio of present age of father to the present age of son is $3:1$.

Step 2. Determine the age of the father to the age of son, when son was $12$ years old.

Age of father when the son was $14$ years old is $42\mathrm{years}$
Age of father when the son was $13$ years old is $41\mathrm{years}$
Age of father when the son was $12$ years old is $40\mathrm{years}$

$\begin{array}{rcl}\mathrm{Ratio}& =& \frac{\mathrm{Age}\mathrm{of}\mathrm{father}}{\mathrm{Age}\mathrm{of}\mathrm{son}}\\ & =& \frac{40}{12}\\ & =& \frac{10}{3}\\ & =& 10:3\end{array}$

Hence, the age of the father to the age of son, when son was $12$ years old is $10:3$.

Step 3: Determine the age of father after $10$ years to the age of son after $10$ years.

$\begin{array}{rcl}\mathrm{Age}\mathrm{of}\mathrm{father}\mathrm{after}10\mathrm{years}& =& \mathrm{Present}\mathrm{age}\mathrm{of}\mathrm{father}+10\\ & =& 42+10\\ & =& 52\mathrm{years}\end{array}$
$\begin{array}{rcl}\mathrm{Age}\mathrm{of}\mathrm{son}\mathrm{after}10\mathrm{years}& =& \mathrm{Present}\mathrm{age}\mathrm{of}\mathrm{son}+10\\ & =& 14+10\\ & =& 24\mathrm{years}\end{array}$

$\begin{array}{rcl}\text{Ratio}& =& \frac{\text{Age of father after}10\text{years}}{\text{Age of son after}10\text{years}}\\ & =& \frac{52}{24}\\ & =& \frac{13}{6}\\ & =& 13:6\end{array}$

Hence, the age of father after $10$ years to the age of son after $10$ years is $13:6$

Step 4. Determine the age of father to the age of son when father was $30$ years old.

When father was $42$ years old, son's age is $14$
When father was $41$ years old, son's age is $13$
When father was $40$ years old, son's age is $12$
When father was $30$ years old, son's age is$12-10=2$
$\begin{array}{rcl}\mathrm{Ratio}& =& \frac{\mathrm{Age}\mathrm{of}\mathrm{father}}{\mathrm{Age}\mathrm{of}\mathrm{son}}\\ & =& \frac{30}{2}\\ & =& \frac{15}{1}\\ & =& 15:1\end{array}$

Hence, the age of father to the age of son when father was $30$ years old is $15:1$.