Question

the sum of two digit number is 9. when we interchange the digits we found that the resulting digit is greater than the original digit by 27. find the two digit number.

Answer 1

Let the digit at ones place of the number be a

Therefore , if sum of digit at tens place and 'a' is 9 . Then digit at tens place = 9-a

We get the number - 10(9-a) + a

When we interchange digits , new number formed is - 10a + (9-a) = 9a + 9

According To Question -

Original number + 27 = New number.

or, 10(9-a) + a +27 = 9a + 9

or, 90 - 10a + a +27 = 9a + 9

or, 117 - 9a = 9a + 9

or, 117 - 9 = 9a + 9a

or, 108 = 18 a

or, a = 108/18

or, a = 6

Therefore the number is -

10(9-a)+a = 10(9-6)+6= 10×3 +6 = 30+6 = 36

When we interchange the digits the new number is 63 and 63 - 36 = 27

Answer) The number is 36.