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

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
`(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 =
`(1)/(x)`

Reciprocal of first integer =
`(1)/(2x)`

Given that sum of reciprocal =
`(3)/(10)`

`(1)/(x)+(1)/(2 x)=(3)/(10)`

On solving above equation for x,

`(2+1)/(2 x)=(3)/(10)`

`(3)/(2 x)=(3)/(10)`

2x=10

x=5

First integer = x = 5

Second integer = 2x = 10

Hence two required integers are 5 and 10.