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ANSWER IS 65
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the two digit number is 65
Step-by-step explanation:
Sum of the digits of a two digit number is 11
Let, the first digit is x and the second digit is y
Then, x+y = 11 ------- (1)
The number is 10x + y
If we interchange the digits then the resulting number is 10y + x
The resulting number is less than the original number by 9
Then, (10x + y) - (10y + x) = 9
=> 10x + y - 10y - x = 9
=> 9x -9y = 9
=> x - y = 1 ---------(2)
From (1)+(2) , we get ,
2x = 12 => x = 6
Putting x=6 in equation (1), we get,
6 + y = 11 => y = 5
Hence , the two digit number is (10×6+5) = 65
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