Question

the sum of the digits of a two digit number is 15 the number obtained by interchanging its digits exceeds the given number by 9 find the original number

Answer 1

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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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Answer 2

Answer: 78

Step-by-step explanation: Please follow the attached photo...