Question

Sum of the present ages of Reshma and her mother is $60$ years. Five years ago, her mother's age was $4$ times the age of Reshma. Find their present ages.

Answer 1

Let ${}^{\prime }{x}^{\prime }$ be the present age of Reshma.
Given that the sum of the present ages of Reshma and her mother is $60$ years.
Thus, Reshma's mother's present age is $60-x$
Five years ago, Reshma's age $=x-5$
and her mother's age would be $60-x-5$
Given than five years ago, her mother's age was $4$ times age of Reshma.
Thus, we have
$60-x-5=4(x-5)$
$\Rightarrow$ $55-x=4x-20$
$\Rightarrow$ $55+20=4x+x$
$\Rightarrow$ $75=5x$
$\Rightarrow$ $x=\frac{75}{5}$
$\Rightarrow$ $x=15$
Thus, the present age of Reshma is $15$ years and her mother's is $60-15=45$ years.