Question

One number is 5 times as large as another. The sum of their reciprocals is


`(36)/(5)`
. Find the two numbers.​

Answer 1

`The \ two \ numbers \ are \ (1)/(6) \ and \ (5)/(6)`

Explanation:

Let the two numbers be = x , y

Given:

One of the number is 5 times other number, that is y = 5x ----- ( 1 )

The sum of their reciprocals is 36/5 , that is

`(1)/(x) + (1)/(y) = (36)/(5)` ------ ( 2 )

Substitute y in the second equation.

`(1)/(x) + (1)/(5x) = (36)/(5)\\\\(1 * 5)/(5 * x) + (1)/(5x) = (36)/(5)\\\\(5)/(5x) + (1)/(5x) = (36)/(5)\\\\(5+1)/(5x) = (36)/(5)\\\\(6)/(5x) =(36)/(5)\\\\36 * 5x = 6 * 5\\\\x = (6 * 5)/(36 * 5) = (1)/(6)`

Substitute x in first equation.

`y = 5x\\\\y = 5 * (1)/(6) \\\\y = (5)/(6)`