The sum of the digits of a two-digit number is equal to 15. If these digits switch places then you will get a number that is 27 less than the original number. Find these numbers.

Answer 1

X is the tens digit, Y the ones

10Y+X=10X+Y-27

X+Y=15

X=15-Y

10Y+15-Y=10(15-Y) + Y -27

9Y + 15 = 150 - 10Y + Y -27

18Y = 108

Y=108/18=12/2=6

X=15-6=9

XY=96 69 is 96-27

9+6=15

96 is the number, switch the digits and get 69

Actually, there's a much easier way to do this.

There are only two possibilities. The only single digits that add to 15 are 6&9 and 7&8

Soon as you go below 6 or higher than 9, and you're into 5&10 which aren't both single digits.

Then just narrow it down. 78 and 87 are only 9 apart. That won't work. You need a difference of 27.

So it must be 69 and 96, which is different by exactly 27.