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 two numbers be a and b respectively such that b > a.
According to given condition,
`[ a + b ]/[ b + 1 ] = 3/2`
⇒ 2a + 2b = 3b + 3
⇒ 2a - b = 3                           ......(1)
Also,
`[ b - a ]/a = 1/2` 
⇒ 2b - 2a = a
⇒ 2b - 3a = 0                         .......(2)
Multiplying (1) by 2, We get
4a - 2b = 6                            .......(3)
Adding (2) and (3),We get
      4a - 2b = 6  
+  - 3a + 2b = 0  
        a = 6
Substituting a = 6 in equation (1), We get
2(6) - b = 3
⇒ 12 - b = 3
⇒ b = 9
Thus, the two numbers are 6 and 9 respectively.