The sum of reciprocals of Meena's ages (in years ) 3 years ago and 5 years hence $\frac{1}{3}$. Find her present ages.

Home » The sum of reciprocals of Meena’s ages (in years ) 3 years ago and 5 years hence . Find her present ages.

The sum of reciprocals of Meena’s ages (in years ) 3 years ago and 5 years hence $\frac{1}{3}$ . Find her present ages.

The sum of reciprocals of Meena’s ages (in years ) 3 years ago and 5 years hence $\frac{1}{3}$ . Find her present ages.

Let the present age of Meena be $x$ years

Meena’s age 3 years ago $=(x-3)$ years

Meena’s age 5 years hence $=(x+5)$ years

According to the given condition,

$\frac{1}{x-3}+\frac{1}{x+5}=\frac{1}{3}$
$\Rightarrow \frac{x+5+x-3}{(x-3)(x+5)}=\frac{1}{3}$
$\Rightarrow \frac{2 x+2}{x^{2}+2 x-15}=\frac{1}{3}$
$\Rightarrow x^{2}+2 x-15=6 x+6$
$\Rightarrow x^{2}-4 x-21=0$
$\Rightarrow x^{2}-7 x+3 x-21=0$
$\Rightarrow x(x-7)+3(x-7)=0$
$\Rightarrow(x-7)(x+3)=0$
$\Rightarrow x-7=0$ or $x+3=0$
$\Rightarrow x=7$ or $x=-3$
$\therefore x=7$
(Age cannot be negative)