Question

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

Answer 1

Using the information from the question, one can construct two equations:


`4 z = x` ... (1)


`(1)/(z) + (1)/(x)` ... (2)

by substituting (1) into (2) to find x


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


`(5)/(4z) = (1)/(4)`

\frac{5}{4z} = \frac{1}{4}


`(4z)/(5) = (4)/(1)`


`(4z)/(1) = (20)/(1)`


`z = (20)/(4)`

⇒ z = 5

By substituting value of z into (1)

⇒ 4 (5) = x

⇒ x = 20

Thus the two numbers are 5 & 20

Answer 2

The required numbers are 5 and 20.

Explanation:

Given : One number is four times another number.

Let the first number is 'x'

The reciprocal of the first number is
`(1)/(x)`

and another number is '4x'

The reciprocal of the another number is
`(1)/(4x)`

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

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

Solving the equation,

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

`(5)/(4x)=(1)/(4)`

Cross multiply,

`5* 4=1* 4x`

`20=4x`

`x=(20)/(4)`

`x=5`

Another number is
`4x=5* 4=20`

Therefore, the required numbers are 5 and 20.