Question

a positive integer is twice another. the sum of the reciprocals of the two positive integers is 1/8. find the two integers

Answer 1

Let the integer is x
So, its twice is 2x
So, the reciprocals of the two integers = $\frac{1}{x} \ and \ \frac{1}{2x}$
The sum of the reciprocals of the two positive integers = 1/8


∴ $\frac{1}{x} + \frac{1}{2x} = \frac{1}{8}$
∴ $\frac{2+1}{2x} = \frac{1}{8}$
∴ $\frac{3}{2x} = \frac{1}{8}$
∴ 2x = 24 
∴ x = 12

So, the two integers are 12 and 24