Question

One number is 4 times as large another. The sum of their reciprocals is 45/4. Find the two numbers

Answer 1

9 because 9*5=45 that the answer I hope you like it

Answer 2

Let,
the numbers be "x" and "y"
According to the question,
x = 4y ......................................................equation (1)


`(1)/(x) + (1)/(y)= (45)/(4)`...................................equation (2)

Taking equation (2)

`(1)/(x) + (1)/(y)= (45)/(4)`

Substituting the value of "x" from equation (1), we get,


`(1)/((4y)) + (1)/(y)= (45)/(4)`


`(1)/(4y) + (1)/(y)* (4)/(4) = (45)/(4)`


`(1)/(4y) + (4)/(4y)= (45)/(4)`


`(1+4)/(4y) = (45)/(4)`


`(5)/(4y) = (45)/(4)`

Cross multiplying, we get,


`5*4 = 45*4y`


`20 = 180y`


`(20)/(180) = y`


`(1)/(9) = y`


`y = (1)/(9)`

Now,
Taking equation (1)
x = 4y
Substituting the value of "y", we get


`x = 4( (1)/(9) )`


`x= (4)/(9)`

So, the numbers are
`(1)/(9)` and
`(4)/(9)`