Question 1121078: The sum of the digits of a two digits number is 11.if the digits are interchanged. The number they form decreases by 9.find the number Found 3 solutions by Alan3354, solver91311, greenestamps:Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website! 65
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Reversing a 2 digit number changes the number by 9 times the difference between the digits.
You might want to play around with this a bit to see that it works, since problems like this involving reversing the digits of a 2-digit numbers are common.
You might even want to look at an algebraic proof that the method works....
When the digits of a 2-digit number are reversed, the difference between the original number and the new number is 9 times the difference between the two digits.
In this problem, the sum of the digits is 11; and when the digits are reversed the value of the number decreases by 9. Since 9 is 9*1, the difference between the two digits is 1.
So the two digits have to be 5 and 6; then, since the number decreases when the digits are reversed, the original number was 65.
