Question

The sum of reciprocals of Arjun’s ages 3 years ago and 5 years from now is $\frac{1}{3}$. His present age is ___ years.

• A. 7
• B. 8
• C. 6
• D. 5

Answer 1

The correct option is A

7

Suppose present age of Arjun is $x$ years

His age 3 years ago = $x–3$ years

His age after 5 years = $x+5$ years

Given condition is

$\frac{1}{x-3}+\frac{1}{x+5}=\frac{1}{3}$

$\frac{1}{x-3}+\frac{1}{x+5}=\frac{1}{3}$

$3(2x+2)=(x-3)(x+5)$

$6x+6=x^2+2x-15$

$x^2–4x–21=0$

Solving this quadratic equation, we get $x=7,-3$

Lets ignore negative value for age

Thus, Arjun's present age $=7\text{y}ears$.