Question

A number consists of two digits whose sum is 9.If 9 is added to the number its digits are interchanged. find the number.​

Answer 1

Let the digits at ones place be x

Then the digits at tens place=9-x ..(sum of two digits is 9)

Therefore the number =10 (9-x)+x=90-10x+x=90-9x

Now,Number obtained by reversing the digits=10x+9-x=9x+9

It is given if 9 is subtracted from the number.,it's digits are interchanged.

90-9x-9=9x+9

81-9x=9x+9

81-9=9x+9x

18x=72

x=72/18

x=4

digits at ones place is x=4

tens place=9-x=9-4=5

Thus the number is 54

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Answer 2

Answer:

let the unit digit be x and the tens digit by y

We are told x+y = 9

So the original number is 10y+x

we are told: 10y+x - 9 = 10x + y

9x - 9y = -9

x-y = -1

add and

2x = 8

x = 4 , then in y = 5

so the number is

10y+x

= 10(5) + 4 = 54