The sum of the digits of a two-digit number is 9. If the digits are reversed, then the number is increased by 27. Find the number.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 36.
We know,
Let the two-digit number be represented as 10x + y
Now,
Sum of digits = 9
⇒ x + y = 9
Reversing digits increases the number by 27
⇒ 10y + x = 10x + y + 27
Now, solving for x and y
⇒ 10y + x - 10x - y = 27
⇒ 9y - 9x = 27
⇒ y - x = 3
Adding both equations;
⇒ (x + y) + (y - x) = 9 + 3
⇒ 2y = 12
⇒ y = 6
Putting the value of y = 6,
⇒ x + y = 9
⇒ x = 9 - 6
⇒ x = 3
Hence, the number = 10x + y
⇒ 10 × 3 + 6
⇒ 30 + 6 = 36