Question

7) Vivek is older than Kishore by 5 years. The sum of the reciprocals of their​

Answer 1

Consider Vivek's age as = x

and Kishor's at as = x+5

now, as they mentioned there reciprocals sum is

= 1/6

so, let us take the reciprocals of there age

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

• (x+5 + x/ x²+6x) = 1/6

• 6(2x+5) = 1(x²+6x)

• 12x+30 = x²+6x

• x²+6x-12x-30 = 0

• x²-6x-30 =0

i am sorry can't type more i have a fracture!

Answer 2

Correct question :-

Vivek is older than Kishore by 5 years. The sum of the reciprocal of their age is 1/6 find their present age.

Solution :-

Let the present age of Kishor be x years.

∴ The present age of Vivek is( x + 5 ) years

According to the question :-

$\longrightarrow \sf \dfrac{1}{x} + \dfrac{1}{x+5} = \dfrac{1}{6} \\\\\longrightarrow \dfrac{x+5+x}{x(x+5)} = \dfrac{1}{6} \\\\\longrightarrow \dfrac{2x+5}{x(x+5)} = \dfrac{1}{6} \\\\\longrightarrow 6(2x+5) = x(x+5) \\\\\longrightarrow 12x+30 = x^2+5x \\\\\longrightarrow x^2+5x-12x-30 = 0 \\\\\longrightarrow x^2-7x-30 = 0 \\\\\longrightarrow x^2-10x+3x-30 = 0 \\\\\longrightarrow x(x-10)+3(x-10) = 0 \\\\\longrightarrow (x+3)(x-10) =0 \\\\\longrightarrow \bd x = -3 \ , \ x= 10$

Age cannot be negative.

So, x = 10

Present age of Kishor = 10 years

Present age of Vivek = 15 years