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Sum of the digits of a two-digit number is 9. When we interchange the digits, it is found that the resulting new number is greater than the original number by 27. What is the two-digit number?

*Concept: Any two-digit number contains is of the form "ab" where the "b" is in the "ones" place and "A" is in the "tens" place. *

*The value of "a" is 10a and the value of "b" is 1.*

According to the question, the sum of the digits of the two-digit number is 9.

Therefore, we assume that the digit units place be "9-x" and at the ten’s place be "x".

Then, the sum of the digits = 9 - x + x = 9 (As given in the question)

Then, the original number = 10x + (9-x) = 9x+9

This is because the value of x will be "10 times x as it is on ten's place"

When we interchange the digits, the digits at one’s place and tens place will be x and 9-x.

Thus, the new number will be 10(9 - x)+x = 90-9x

Now, New Number = Original Number + 27

90 -9x = 9x + 9+ 27

90 – 9x = 9x + 36

90- 36 = 18x

X = 3 and 9-x = 6

Thus, the two digit number is 9x + 9 = 9 (3)+9 =36

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