Mathematical Puzzles
Hard
3 min
A two-digit number has digits whose sum is 11. When the digits are reversed, the new number is 27 greater than the original number. What is the original number?
Hint
Let the tens digit be x and the units digit be y.
Answer
47
Explanation
Let the number be 10x + y. The reversed number is 10y + x. Their difference is 27 and x + y = 11. Solving gives x = 4 and y = 7.
Step-by-Step Solution
x + y = 11.
(10y + x) - (10x + y) = 27.
9(y - x) = 27.
y - x = 3.
Solving x + y = 11 and y - x = 3 gives x = 4, y = 7.
Therefore the number is 47.
(10y + x) - (10x + y) = 27.
9(y - x) = 27.
y - x = 3.
Solving x + y = 11 and y - x = 3 gives x = 4, y = 7.
Therefore the number is 47.