Question

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

Answer 1

Answer:

The numbers are 5 and 20.

Step-by-step explanation:

To find : What are the numbers?

Solution :

Let the one number be 'x'.

The reciprocal is $\frac{1}{x}$

The another number be 'y'.

The reciprocal is $\frac{1}{y}$

One number is four times another number.

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

The sum of their reciprocals is $\frac{1}{4}$.

i.e. $\frac{1}{x}+\frac{1}{y}=\frac{1}{4}$ ....(2)

Substitute (1) in (2),

$\frac{1}{4y}+\frac{1}{y}=\frac{1}{4}$

$\frac{1+4}{4y}=\frac{1}{4}$

$4y=20$

$y=5$

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

Therefore, the numbers are 5 and 20.

Answer 2

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.