Question

the sum of the 2 digit number is 9. when we interchange the digit it is found, that the resulting number is greatter than the original number by 27. what is the 2 digit number

Answer 1

Let the digit in the tens place be x and the digit in the ones place be y.

x+y=9

y = 9-x

The original number = 10x+y

Number obtained by interchanging the digits = 10y+x

10x+y + 27 = 10y+x

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

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

9x + 36 = 90 - 9x

9x + 9x = 90 - 36

18x = 54

x = 3

y = 9-x = 9-3 = 6

Therefore the original no = 10x+y = 30 + 6 = 36

The new no = 10y+x = 60 + 3 = 63

Answer 2

Hope this helps you

Let the digit in the tens place be x and the digit in the ones place be y.

x+y=9

y = 9-x

The original number = 10x+y

Number obtained by interchanging the digits = 10y+x

10x+y + 27 = 10y+x

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

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

9x + 36 = 90 - 9x

9x + 9x = 90 - 36

18x = 54

x = 3

y = 9-x = 9-3 = 6

Therefore the original no = 10x+y = 30 + 6 = 36

The new number = 10y+x = 60 + 3 = 63