Question

The sum of the digits of a two digit number is 9. the number obtained by reversing the digits is 9 less than the original number . find the number

Answer 1

Let the unit digit be X.
Then the tense digit be(9-X)
Original number = 10×tense digit+ unit digit
= 10(9-X) + X
= 90-10X + X
= 90-9X
After interchanging
Unit digit be (9-X)
Tense digit be X
New number = 10×tense digit+unit digit
= 10×X+ 9-X
= 9X+9
A/Q (9X+9) +9 = 90-9X
or 9X+18 = 90-9X
or 9X+9X = 90-18
or 18X = 72
therefore X = 72/18 = 4
Unit digit = X = 4
Tense digit = 9-4 = 5
so, number = 54