Question

The digit of a two digit number differ by 5. if the digits are reversed, the sum of the two numbers is 99. find the number?

Answer 1

Let us assume, the x and y are the two digits of a two-digit number.

Therefore, the two-digit number = 10x + y and reversed number = 10y + x

Given:
x - y = 5 -------------1

Also given:
10x + y + 10y + x = 99
11x + 11y = 99
x + y = 9 --------------2

Adding equation 1 and equation 2
2x = 14
x = 7

Therefore, y = x - 5 = 7 - 5  = 2
Therefore, the two-digit number = 10x + y = 10*7 + 2 = 72