Question

The sum of the digits of a two-digit number is 12. The number obtained by interchanging its digits exceeds the given number by 18. 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 = 12                         ……….(i)
Number obtained on reversing its digits = (10y + x)
∴ (10y + x) - (10x + y) = 18
⇒10y + x – 10x – y = 18
⇒9y – 9x = 18
⇒y – x = 2                        ……..(ii)
On adding (i) and (ii), we get:
2y = 14
⇒y = 7
On substituting y = 7 in (i) we get
x + 7 = 12
⇒ x = (12 - 7) = 5
Number = (10x + y) = 10 × 5 + 7 = 50 + 7 = 57
Hence, the required number is 57.