The sum of the reciprocals of Rehmans ages, (in years) 3 years ago and 5 years from now is `1/3dot`Find his present age.

Explanation

Let Arun's present age be x years.
Arun's age 3 years ago `=(x-3)` years.
Arun's age 5 years hence `=(x+5)` years.
`:." "(1)/((x-3))+(1)/((x+5))=(1)/(3)`
`implies" "((x+5)+(x-3))/((x-3)(x+5))=(1)/(3)implies(x-3)(x+5)=6(x+1)`
`implies" "x^(2)+2x-15=6x+6impliesx^(2)-4x-21=0`
`implies" "x^(2)-7x+3x-21=0impliesx(x-7)+3(x-7)=0`
`implies" "(x-7)(x+3)=0impliesx-7=0" or "x+3=0`
`implies" "x=7" or "x=-3`
`implies" "x=7" "[because" age cannot be negative"]`
Hence, Arun's present age is 7 years.