Question

The present ages of Ramesh and his elder brother are in the ratio 5:7. After 5 years, the ratio of their ages will be 3:4. Find their present ages?

Answer 1

Hint: The present ages of Ramesh and his elder brother are in the ratio 5:7 so converting the ratio to number by multiplying each number in the ratio by x so the present age of Ramesh becomes 5x and his elder brother is 7x. Now, after 5 years, the age of Ramesh and his elder brother is the addition of 5 in their ages before 5 years. Now, take the ratio of the ages of Ramesh and his elder brother and equate it to $\dfrac{3}{4}$. In this way, we will get the value of x and hence their present ages.

Complete step by step solution:
The present ages of Ramesh and his elder brother are given in the following ratio:
5:7
Now, converting the above ratio to number by multiplying each number in the ratio to x and we get,
$5x,7x$
From the above, the present ages of Ramesh and his elder brother is $5x\And 7x$ respectively.
After 5 years, the age of Ramesh and his elder brother respectively is as follows:
$\begin{align}
  & 5x+5; \\
 & 7x+5 \\
\end{align}$
Now, taking the ratio of the above ages and equating the above ratio to 3:4 we get,
$\Rightarrow \dfrac{5x+5}{7x+5}=\dfrac{3}{4}$
Cross multiplying the above equation we get,
$\begin{align}
  & \Rightarrow 4\left( 5x+5 \right)=3\left( 7x+5 \right) \\
 & \Rightarrow 20x+20=21x+15 \\
\end{align}$
Rearranging the above equation in such a way so that x terms on one side of the equation and the constant terms on another side of the equation.
$\begin{align}
  & \Rightarrow 21x-20x=20-15 \\
 & \Rightarrow x=5 \\
\end{align}$
Now, substituting the above value of x in $5x,7x$ we get,
$\begin{align}
  & \Rightarrow 5\left( 5 \right),7\left( 5 \right) \\
 & =25,35 \\
\end{align}$
Hence, the present age of Ramesh is 25 years and the present age of his elder brother is 35 years.

Note: Always remember that age of a person is not defined in decimals so if you are getting the age of a person in decimal points then it means you have made some mistake. So, this is one of the methods through which you can check the age of the individuals.