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

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

...................................equation (2)

Taking equation (2)


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











Cross multiplying, we get,











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





So, the numbers are  and