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:

Correct option is B

Given:

Sum of digits = 15

Interchanged number exceeds the original by 9

Solution:

x + y = 15

(10y + x) - (10x + y) = 9

From (2)

(10y + x) - (10x + y) = 9

10y + x - 10x - y = 9

9y - 9x = 9

y - x = 1

x + y = 15

2y = 16

y = 8

x = 7

10x + y = 10 $$\times$$​ 7 + 8 = 78