Question

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

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.

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