If n is a 3-digit integer, and the result of reversing the digits of n is the number m, what is the maximum value of n-m? show step by step

The maximum value of N-M will be 792

Step-by-step explanation:

For N - M to be maximum

N must be very large and M must be very small

largest 3 numbers occur in 900's and smallest 3 digit numbers occur in 100's

so we need such an N which starts with 9 and ends with 1 so that on reversing it produces a number starting with 1.

If N = 901 , M will be 109

N - M = 792

This is the largest possible value of N - M

All other values of N-M will give a smaller value than 792.