SOLUTION: the sum of the digits of two digit number is 9.if the digits are reversed the new number is decresed by 9.find the number.
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Question 615680: the sum of the digits of two digit number is 9.if the digits are reversed the new number is decresed by 9.find the number.
Answer by Maths68(1474) (Show Source): You can put this solution on YOUR website!
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
======
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
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