Question

One number is four times another number. The sum of their reciprocals is 1/4 . What are the numbers?

Answer 1

If one number is x the other is 4x. I read the sum of their reciprocals as ¼=1/x+1/(4x).
Multiply through by 4x: x=4+1=5. So the numbers are 5 and 20.

Answer 2

The numbers are 5 and 20.

Explanation:

To find : What are the numbers?

Solution :

Let the one number be 'x'.

The reciprocal is
`(1)/(x)`

The another number be 'y'.

The reciprocal is
`(1)/(y)`

One number is four times another number.

i.e.
`x=4y` .....(1)

The sum of their reciprocals is
`(1)/(4)`.

i.e.
`(1)/(x)+(1)/(y)=(1)/(4)` ....(2)

Substitute (1) in (2),

`(1)/(4y)+(1)/(y)=(1)/(4)`

`(1+4)/(4y)=(1)/(4)`

`4y=20`

`y=5`

One number is 4y=4(5)=20.

Therefore, the numbers are 5 and 20.