Question

The present age of Rafi and Fathima are in the ratio $7:5$. Ten years later the ratio of their ages will be $9:7$. Find their present ages?

Answer 1

Since the present ratio of ages of Rafi and Fathima is $7:5$.
We may take, Rafi's age to be $7x$ and the Fathima's age to be $5x$
(Note that ratio of $7x$ and $5x$ is $7x:5x$ and which is same as $7:5$)
After $10$ years Rafi's age $=7x+10$
And Fathima's age $=5x+!0$
After $10$ years, the ratio of Rafi's age and Fathima's age is $7x+10:5x+10$
But according to the given data this ratio is equal to $9:7$
$\Rightarrow$ $7x+10:5x+10=9:7$
ie., $7(7x+10)=9(5x+10)$
$\Rightarrow$ $49x+70=45x+90$
Did you notice that in the above equation we have algebraic expressions on both sides.
Note let us learn how to solve such equations.
The above equation is $49x+70=45x+90$
$\Rightarrow$ $49x-45x=90-70$ (Transposing $70$ to RHS and $45$ to LHS)
$\therefore$ $4x=20$
$\therefore$ $x=\frac{20}{4}=5$
Therefore Rafi's age $=7x=7\times 5=35$ years
And Fathima's age $=5x=5\times 25$ years