SOLUTION: the sum of the digits of a two digit number is 15. if the digits are interchange the result exceeds the original number by 9. find the number.

Question 259429: the sum of the digits of a two digit number is 15. if the digits are interchange the result exceeds the original number by 9. find the number.
Answer by palanisamy(496) (Show Source): You can put this solution on YOUR website!
Let the number be xy.
Given,the sum of the digits of a two digit number is 15.
x+y = 15 ...(1)
Also, if the digits are interchanged the result exceeds the original number by 9.
10y+x=10x+y+9
10y+x-10x-y=9
9y-9x=9
y-x=1 ...(2)
(1)+(2) => 2y = 16
y = 16/2 = 8
(1) => x+8=15
x=15-8=7
Therefore the given number is 78
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