The sum of the reciprocals of Meena's ages (in years) 3 years ago and 5 years hence is

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 $x=-3$

∴ x = 7                 (Age cannot be negative)

Hence, the present age of Meena is 7 years.