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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?

Q.3 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?

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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. 

 

Posted by

Divya Prakash Singh

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