Question

The sum of the reciprocals of Rehman’s ages, (in years) 3 years ago and 5 years from now is 1/3. Find his present age?

• A. 5
• B. 7
• C. 9
• D. 10

Answer 1

Answer:

B. 7

Present age = X

Rehman’s age, (in years) 3 years ago = X - 3

Rehman’s age, (in years) 5 years from now = X + 5

$\frac{1}{X-3}+\frac{1}{X+5}=1/3$

$\frac{(X+5)+(X-3)}{(X+5)(X-3)}=1/3$

$\frac{2x+2}{X^2-3X+5X-15}=1/3$

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

$X^2-4X-21=0$

$(X-7)(X+3)=0$

$X=7 or = -3$

but age never become negative

$X=7$