let the two digit number be 10x+y

and the number obtained by interchanging the position of the digits be 10y+x

According to the question,

(10x+y)−(10y+x)= 9

⇒ 9x−9y=9

⇒ 9(x−y)=9

⇒ (x−y)=1---Eq1

and it is given that x+y=15---Eq2

Upon adding Eq 1 and Eq 2 we get,

(x-y=1)+(x+y=15)⇒2x=16

x=8

Inserting the value of x in the eq (2) we get y=7

So, the original number is 87. Hence option C is correct