Question

The sum of the digits of a two-digit number is 9. If the digits are interchanged the number obtained exceeds the original number by 27. Find the numbers​

Answer 1

Step-by-step explanation:

let the digit at ones place be x.

So digit at tens place be 9-x .

Original number =10(9-x)+x

=90-10x+x

=90-9x. ....i

Number formed after interchanging the digits=

10×x+9-x

10x+9-x

9x+9

A/Q

90-9x+27=9x+9

117-9=9x+9x

108=18x

x=108/18

=6

Now the original number is 90-9×6=90-54=36. (from eq.i)

Answer 2

Answer:

let unit digit be x

let ten 's digit be 9 - x

Step-by-step explanation:

here is

=10(9-x) + x = 90 -10x + x = 90 - 9 x

if we interchanged the digit so ,

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

now , according to the question

9x + 9 + 27 = 90 - 9x

9x + 36 = 90 - 9x

9x - 9x = 90 - 36

x = 54