Question

If a and b are two two-digit positive integers with different values such that a > b, then the difference between the maximum and minimum values of a+b/a-b is​

Answer 1

Given :  a and b are two two-digit positive integers with different values such that a > b

To Find :   the difference between the maximum and minimum values

Solution:

Two digit numbers

10 to 99

(a + b)/(a - b)   is minimum  when a-b  is maximum

a = 99

b = 10

(99 + 10)/(99 - 10)  = 109/89  

(a + b)/(a - b)   is maximum  when a-b  is minimum

a - b  is minimum  

a - b = 1      

(99 +  98 )/(99 - 98)

= 197/1

= 197

197  - 109/89

= 17424/89

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