Question

The age of Ravi and Rahul are in the ratio \[5:7\]. Four years from now, the ratio of their ages will be $3:4$. Find their present age.

Answer 1

Hint: If the age of two persons is given in the form of ratio, for example , $p:q$ , then the age shall be considered as $px$ and $qx$. After considering their ages as $px$ and $qx$ add 4 to $px$ and $qx$ and then equate it to 3,4. As it is given in the question that they both are equal.

Complete step-by-step answer:
Given, the age of Ravi and Rahul are in the ratio \[5:7\].
Let the age of Ravi be $5x$ years and the age of Rahul be $7x$ years.
$4$ years later, age of Ravi will be $\left( {5x + 4} \right)$years and age of Rahul will be $\left( {7x + 4} \right)$years.
As per the question; $4$ years later, the ratio of their ages will be $3:4$.
$\therefore {{5x + 4}}{{7x + 4}} = {3}{4}$
$ \Rightarrow 4\left( {5x + 4} \right) = 3\left( {7x + 4} \right)$
$ \Rightarrow 20x + 16 = 21x + 12$
$ \Rightarrow 16 - 12 = 21x - 20x$
$ \Rightarrow x = 4$

Therefore, Ravi’s present age $ = 5x = 5 \times 4 = 20$years
And Rahul’s present age $ = 7x = 7 \times 4 = 28$years

Note: If you are assuming the current age of a person to be $x$ years , then his age after $n$ years will be $\left( {x + n} \right)$ years, while before $n$ years his age will be $\left( {x - n} \right)$ years.