Question

The difference of a two digit number is 5, also the number obtained by reversing the digits is 9 less than three times of the original number. find the number

Answer 1

Let us assume, x and y are the two digits of the two-digit number and let us assume, y > x

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

Given:

y - x = 5 ------------1

Also given:

10y + x = 3 (10x + y) - 9

10y + x = 30x + 3y - 9

29x - 7y = 9 -------------------2

Multiply equation 1 by 7

 7y - 7x = 35 -------------3

adding equation 2 and equation 3

22x = 44

x = 2

Therefore, y = 5 + x = 5 + 2 = 7

Therefore, the two-digit number = 10x + y = 10*2 + 7 = 27