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

Let the tens place digit be a and the units place digit be b.
Then, the number is (10a + b).

​Given:
a + b = 15 ... (1)

When the digits are interchanged the number will be (10 b + a).
Given:
10a + b + 9 = 10 b + a
∴ 10a - a + b - 10b = -9
9a - 9b = -9​
a - b = -1 ... (2)

Adding equations (1) and (2):

a + b = 15
a - b = -1
2a = 14
∴ a = 7

Using a = 7 in equation (2):
7 - b = -1
∴ b = 8

Original number = 10a+b = 10 $\times$ 7 + 8 = 78