Question

Johnny is $\dfrac{2}{3}$ of the age of his elder brother. If the difference in their ages is 4 years. How old is each boy?

Answer 1

Hint: We first assume the age of Johnny and then calculate his elder brother’s age. We find the difference which is equal to 4. We solve the equation to find the value of the variable $x$.

Complete step by step solution:
Let us assume the ages of Johnny and his elder brother.
We take the age of his elder brother to be $x$. Johnny is $\dfrac{2}{3}$ of the age of his elder brother.
Therefore, the age of Johnny is $\dfrac{2x}{3}$.
The difference in their ages is 4 years. This means $x-\dfrac{2x}{3}=4$.
We solve the equation $x-\dfrac{2x}{3}=4$ to find the value of $x$.
So, $x-\dfrac{2x}{3}=4$ gives $\dfrac{x}{3}=4$.
We now complete the cross multiplication to find the value of $x$.
We have $x=3\times 4=12$.
The age of the elder brother Johnny is 12 years. The age of Johnny is \[\dfrac{2x}{3}=\dfrac{2\times 12}{3}=8\].
Therefore, the age of Johnny and his elder brother is 8years and 12years respectively.

Note:
We need to remember that we can also use the variable for the age of Johnny. The relation would have been that his elder brother is $\dfrac{3}{2}$ of Johnny’s age.