Question

When the greater of the two numbers increased by 1divides the sum of the numbers, the result is `3/2`. When the difference of these numbers is divided by the smaller, the result `1/2`. Find the numbers.

Answer 1

Let the greater number = x, and the smaller number = y.

`(x+y)/(x+1) = 3/2`

2(x + y) = 3(x + 1)

2x + 2y = 3x + 3

2y = x + 3

x = 2y − 3     ...(1)

`(x-y)/y = 1/2`

2(x − y) = y

2x − 2y = y

2x = 3y

`x = 3/2y`     ...(2)

`2y - 3 = 3/2y`

4y − 6 = 3y

y = 6

`x = 3/2 xx 6 = 9`

9 and 6