The sum of the digits of a two−digit number is 9. The number obtained by interchanging its digits exceeds the given number by 45, then the original number is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 27.
Let the two-digit number be represented as (10x + y)
The sum of the digits is 9:
⇒ x + y = 9....(1)
The number after interchanging is 10y + x, and it exceeds the original number by 45
⇒ (10y + x) - (10x + y) = 45
⇒ 9y - 9x = 45
⇒ y - x = 5....(2)
On solving equations 1 and 2
⇒ 2y = 14
⇒ y = 7 then,
⇒ x = 2
Thus, the original number = 10x + y = 20 + 7 = 27