Question

the sum of the digits in a two digits number 9. the number obtained by interchanging the digits exceeds the original number by 27. find the two digits number

Answer 1

let x is unit digit and y is ten digit

and number is x+10y

ATQ

x+y=9

x=9-y______(i)

(x+10y)+27=(10x+y)______(ii)

putting the value of x in equation ii

(9-y+10y)+27=90-10y+y

9y+36=90-9y

9y+9y=90-36

18y=54

y=3

x=9-y

x=9-3=6

Hence the number is

x+10y

6+3×10

6+30=36

Answer 2

Answer:

Let the two digit number be 10x + y

Given that the sum of the digits is 9

x + y = 9 (equation 1)

Given that the number obtained by interchanging the digits exceeds the given number by 27

10y + x = 10x + y + 27 

9x - 9y = - 27

taking 9 as common

x - y = - 3 (equation 2)

Adding equation 1 and 2

x + y = 9

x - y = - 3

2x = 6

x = 3

3 + y = 9

y = 6

The number is 10x + y is