Question

The sum of the digits of a two-digit number is 15. If the number formed by reversing the
digits is less than the original number by 27. Find the original number and reversed
number, find the product of their unit place digits.

Answer 1

let tens digit of the original number be x

so original number,

10(x) + (15-x)

reversing digits mean

10(15-x) + x

therefore

[10(x) + (15-x)]-[10(15-x)+x] = 27.

10x + 15-x - 150+10x-x = 27.

10x + 10x + 15 - 150 -x - x = 27.

20x - 135 -2x = 27.

18x - 135 = 27.

18x = 27 + 135.

18x = 162.

x = 162/18.

x = 9.

original number = 10(x) + (15-x)

= 10(9) + (15-9)

= 90+6

= 96