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Mathematical Puzzles Hard 3 min

A two-digit number has digits whose sum is 11. Reversing the digits increases the number by 27. 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 9(y-x)=27, so y-x=3. Together with x+y=11 gives x=4 and y=7.

Step-by-Step Solution

x+y=11.
9(y-x)=27.
y-x=3.
Adding gives 2y=14, so y=7.
x=4.
Number = 47.
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