Question

the sum of the 2 digit number is 9. If the digits of the number are reversed the new number is decreased by 9 . Find the number

Answer 1

Let x be the tens digit

and y be the unit digit

So,

10x + y = number

The sum of the digits of a number is 9.

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

Reversing the digits decrease the number by 9.

10y + x = 10x + y - 9

10y - y = 10x - x - 9

9y = 9x - 9

9y = 9(x - 1)

Divide above equation by 9, we have

y = x - 1

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

Add (1) and (2)

y - x = -1

x + y = 9

2y=8.........(2)

Divide by 2 both sides

2y/2=8/2

y = 4

Put the value of x in (1)

x+y=9

x+4=9

x=9-4

x=5

Digits are 5 and 4

and number is 54

Check

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The sum of the digits of a number is 9

5+4=9

9=9

Reversing the digits decrease the number by 9.

45=54-9

45=45