Question

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. Find the number.

Answer 1

Let the tens and the units digits of the required number be x and y, respectively.
Required number = (10x + y)
x + y = 15                  ……….(i)
Number obtained on reversing its digits = (10y + x)
∴ (10y + x) - (10x + y) = 9
⇒10y + x – 10x – y = 9
⇒9y – 9x = 9

⇒y – x = 1                ……..(ii)
On adding (i) and (ii), we get:
2y = 16
⇒y = 8
On substituting y = 8 in (i) we get
x + 8 = 15
⇒ x = (15 - 8) = 7
Number = (10x + y) = 10 × 7 + 8 = 70 + 8 = 78
Hence, the required number is 78.