Question

vivek is older than kishor by 5 years. The sum of reciprocals of their aahe is 1/6. Find their present ages.

Answer 1

Let, age of kishor= x
age if vivek = y
according to question,

y-x = 5

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

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

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

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

solve this u get.
x= -3 , 10

age of kishor = 10 years
age if vivek = 15 years

hope u get ur answer :-)

Answer 2

Let the age of Kishor be x
Then age of vivek = x+5

According to question
$\frac{1}{x} + \frac{1}{x + 5} = \frac{1}{6} \\ \frac{(x + 5) + x}{x(x + 5)} = \frac{1}{6} \\ \frac{x + 5 + x}{ {x }^{2} + 5x} = \frac{1}{6} \\ 12x + 30 = {x}^{2} + 5x \\ {x}^{2} - 7x - 30 = 0 \\ {x}^{2} - 10x + 3x - 30 = 0 \\ x(x - 10) + 3(x - 10) = 0 \\ (x - 10)(x + 3) = 0 \\ x = 10 \: or \: \: x = - 3$
However age cannot be negative.
Therefore x = 10.

Age of Kishore = x = 10 years
Age of Vivek = x+5
= 10+5
= 15 years.

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