The sum of the digits of a two-digit number is 15.The number obtained by interchanging the digits exceeds the given number by 9.The number is

(a) 96 (b) 69 (c) 87 (d)78

Let the number be 10x+y.
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
$\Rightarrow$ 9y-9x=9
$\Rightarrow$ y-x=1 ...(2)
Adding equations (1) and (2), 2y = 16
$\Rightarrow$ y = ​​8
Now, x+8=15
$\Rightarrow$ x=15-8=7
Therefore, the given number is 10x+y=10 $\times$ 7+8= 78