The sum of the digits of a two digit number is 12. If the new number formed by reversing the digits is greater than the original number by 18, find the original number. Check your solution.

Let the digit in the ones place be x.
Then the digit in the tens place will be 12 – x.
Therefore, the original number = 10(12 - x) + x = 120 – 10x + x = 120 - 9x.
And, the new number = 10 x + (12 - x) = 10x + 12 – x = 9x + 12.
By the given condition,
New number = original number + 18
9x + 12 = 120 – 9x + 18
9x + 12 = 138 – 9x
9x + 9x = 138 – 12 (Transposing 9x and 12)
18x = 126
(Dividing both sides by 18)

x = 7
Thus, ones digit is 7 and tens digit is 12 - 7 = 5. Hence, the required number is 57.
Check: (1) 5 + 7 = 12 is the sum of the digit.
(2) New number = 75.
Difference between the original number and new number = 75 – 57 = 18.
\\ The new number is 18 more than the original number.