Question

The product of two positive numbers is 9. The reciprocal of

one of these numbers is 4 times the reciprocal of the other number. What is the sum of the two numbers?

Answer 1

Explanation:

Let x and y be the two positive numbers.

Now according to the given condition we have:

x.y=9........(1)

1/x=4.1/y......(2)

Now from (1) we have,

1/x=y/9

Substituting 1/x=y/9 in (2) we have,

y/9=4/y

Solving this we have

y^2=36

y=+6 and y=-6

But neglecting the negative value as we are given in the question that the numbers are positive. So

y=6

Substituting y=6 in (1) we have,

x.6=9

Solving which gives

x=3/2

So the numbers are 3/2 and 6