The difference between two natural numbers is 6. if the sum of their reciprocals is 5/8,find the numbers.

Let two natural numbers are x and y.

Given: The difference between two natural numbers is 6, Therefore,

And, the sum of their reciprocals is 5/8, so,

Substitute value of y = x+6 from equation (1) in equation (2), we get,

Since, -24/5 is not natural number. So, we will take y = 2.

Now, putting value of y = 2, in equation (1), we get,

Thus, the numbers are 8 and 2.