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

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Answer 2

Answer:

Kishor's present age is 10 years

,Vivek's present  age =15 years

Step-by-step explanation:

Given :

vivek is older than kishor by 5 years.

The sum of reciprocals of their age is 1/6.

To Find:Find their present ages  

Solution :

Let Kishor's present  age be x

Since we are given that vivek is older than kishor by 5 years.

So,Vivek's present age = x+5

since we are given that The sum of reciprocals of their age is 1/6.

⇒$\frac{1}{x} +\frac{1}{x+5} =\frac{1}{6}$

⇒$\frac{2x+5}{(x)(x+5)} =\frac{1}{6}$

$\frac{2x+5}{x^{2}+5x} =\frac{1}{6}$

$6*(2x+5)=x^{2}+5x$

$12x+30=x^{2}+5x$

$x^{2}-7x-30=0$

$x^{2}-10x+3x-30=0$

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

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

so, x = -3,10

So, we will neglect the negative value since we age cannot be negative

So. Kishor's present age is 10 years

,Vivek's present  age = x+5 =10 +5=15 years