Vivek is older than Kishor by 5 years. The sum of the reciprocals of their ages is `1/6`. Find their present age.

Answer

The present ages of Kishor and Vivek are 10 years and 15 respectively.

Explanation

Let the present age of Kishor be x years. Then the present gae of Vivek is (x+5) years. The multiplicative inverses (reciprocals) of their ages are `(1)/(x)and(1)/(x+5)` respectively.
From the given condition,
`(1)/(x)+(1)/(x+5)=(1)/(6)`
`:.(x+5+x)/(x(x+5))=(1)/(6)`
`:.(2x+5)/(x^(2)+5x)=(1)/(6)`
`:.6(2x+5)=1(x^(2)+5x).......` (By cross multiplication)
`:.12x+30=x^(2)+5x`
`:.x^(2)+5x=12x-30`
`:.x^(2)+5x-12x-30=0`
`:.x^(2)-7x-30=0`
`x^(2)-10x+3x-30=0`
`:.x(x-10)+3(x-10)=0`
`:.(x-10)(x+3)=0`
`:.x-10=0orx+3=0`
`:.x=10orx=-3`
But the age cannot be negative.
`:.=-3` is unacceptable.
`:.x=10andx+5=10+5=15`