Sum of the digits of a two digit number is 11. when we interchange the digits it is found that the resulting number is less than the original number by 9. what is the two digit number.
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Let the ones digit be x
tens digit = 11-x
Number formed = 10(11-x) + x = 110-10x+x = 110-9x
By interchanging digits,
ones digit = 11-x
tens digit = x
New number = 10x - 11 - x = 9x - 11
According to the question,
9x - 11 - (110-9x) = 9
9x-11-110+9x = 9
18x - 121 = 9
18x = 9+121 = 130
x = 130/18
tens digit = 11-x
Number formed = 10(11-x) + x = 110-10x+x = 110-9x
By interchanging digits,
ones digit = 11-x
tens digit = x
New number = 10x - 11 - x = 9x - 11
According to the question,
9x - 11 - (110-9x) = 9
9x-11-110+9x = 9
18x - 121 = 9
18x = 9+121 = 130
x = 130/18
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