Question

The number obtained by interchanging the digits of a 2-digit number is 9 more than the original
number. If the sum of the digits is 9. then find the original number

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Answer 1

Answer:

45

Step-by-step explanation:

Let the number be xy i.e 10x+y

Number after interchanging digits is 10y+x

Given ;

10y+x=9+10x+y

9y-9x=9

y-x=1

Given x+y =9

On solving

y=5;x=4

Answer 2

Answer:

The original number is "45"

Step-by-step explanation:

Let the original number be 10x+y

Given, x+y = 9 ........ (1)

According to the problem,

10y+x = 10x+y + 9 ( 10y+x is the no. obtained by inter changing the digits)

10y-y = 10x-x + 9

9y = 9x + 9

9y-9x = 9

9(y-x)= 9

y-x = 9/9

y-x = 1 ........ (2)

Adding (1) & (2),

x+y = 9

-x+y = 1

-------------

2y = 10

y = 10/2

*y = 5

substitute y = 5 in (1)

x+5 = 9

x = 9-5

*x = 4

Therefore, the original number is,

10x + y=10(4) + (5) = 40+5 = *45