Question

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

Answer 1

Answer:

Given that sum of the two digits is 9.

Let us assume the digit of units place be x.

Then the digit of tens place will be 9-x.

Thus the two digit number is 10(9-x) + x

Now if we reverse the digits, the number becomes   10x + (9-x).

As per the question,

                10x + (9-x) = 10(9-x) + x + 27

or               9x + 9 = 90 - 10x + x + 27

or               9x + 9 = 117 - 9x

Transposing -9x to the LHS and 9 to the RHS:

                 9x + 9x = 117 - 9

or                   18x  =  108

                            x = 6

Thus two digit number is 36.