Question

a positive integer is twice another. Thhe sum of the reciprocals of the positive integers is 3/10. Find the two integers

Answer 1

Answer:

Two required integers are 5 and 10.

Solution:

Given that a positive integer is twice another. The sum of the reciprocals of the positive integers is $\frac{3}{10}$

We have to find the two integers.

Let assume that one integer = x

Since another integer is twice of first one, so second integer = 2x

Reciprocal of first integer = $\frac{1}{x}$

Reciprocal of first integer = $\frac{1}{2x}$

Given that sum of reciprocal = $\frac{3}{10}$

$\frac{1}{x}+\frac{1}{2 x}=\frac{3}{10}$

On solving above equation for x,

$\frac{2+1}{2 x}=\frac{3}{10}$

$\frac{3}{2 x}=\frac{3}{10}$

2x=10

x=5

First integer = x = 5

Second integer = 2x = 10

Hence two required integers are 5 and 10.