Question

Vivek is older than kishor by 5years. The sum of the reciprocals of their ages is1/6. Find their present ages

Answer 1

Let the age of Kishor be x years

And age of Vivek be x + 5 years

Now according to the question :

1 / x + 1 / x + 5 = 1 / 6

L.C.M = x ( x + 5 ) = x^2 + 5x

x + 5 + x / x^2 + 5x = 1 / 6

2x + 5 / x^2 + 5x = 1 / 6

On cross multiplying we get :

6 ( 2x + 5 ) = x^2 + 5x

12x + 30 = x^2 + 5x

12x - 5x = x^2 - 30

7x = x^2 - 30

x^2 - 7x - 30 = 0

Splitting the middle term

x^2 - 10x + 3x - 30

x ( x - 10 ) + 3 ( x - 10 )

( x + 3 ) ( x - 10 ) = 0

x = - 3 or x = 10

we should neglect the negative value.

so x = 10

x + 5 = 10 + 5 = 15

So Vivek is 15 years old and Kishor is 10 years old.

Hope it helps.

Have a good day buddy.

Answer 2

Hi ,

Let the age of Kishore = x years

Vivek age = ( x + 5 ) years

according to the problem given ,

sum of reciprocals = 1/6

1/x + 1/( x + 5 ) = 1/6

( x + 5 + x )/[ ( x ( x + 5 ) ] = 1/6

6( 2x + 5 ) = x(x + 5 )

12x + 30 = x² + 5x

x² + 5x - 12x - 30 = 0

x² - 7x - 30 = 0

x² - 10x + 3x - 30 = 0

x( x - 10 ) + 3(x - 10 ) = 0

( x - 10 )( x + 3 ) = 0

Therefore ,

x - 10 = 0 or x + 3 = 0

x = 10 or x = -3

age should not be negative.

Therefore ,

age of Kishore = x = 10 years

age of Vivek = x + 5 = 10 + 5 = 15 years

I hope this helps you.

: )