When you reverse the digits in a certain two-digit number you increase its value by 27. Find the number if the sum of its digits is 11.

Answer 1

If the original number is XY, 10X+Y+27 = 10Y+X and X+Y=11 or X=11-Y.

10X+Y+27=10Y+X -> 27=9Y-9X -> 3=Y-X -> 3=Y-(11-Y) -> 3=2Y-11 -> 14=2Y -> 7=Y, so 4=X

The number is 47