Let tens place digit be y and the units place be x.

∴ Our number is (10y + x)

Our given first condition is that sum of the digits of a two-digit number is 15.

∴ By given condition,

y + x = 15 …(1)

Our given second condition is that the number obtained by interchanging its digits exceeds the given number by 9.

∴ By given condition,

10y + x + 9 = 10 x + y
∴ 10y - y + x - 10x = -9
9y - 9x = -9​
y - x = -1 …(2)

Solving 1 and 2 simultaneously, we get,

∴ y = 7 and x = 8

∴ Our number = (10 × 7 + 8) = 78

Hence, our number is 78.

(Answer given is 48 but correct answer is 78)