A number consists of two digits. The digit at the tens place is twice the…
2016
A number consists of two digits. The digit at the tens place is twice the digit at the ones place. If 27 is added to the number, the digits interchange their places. Find the number.
- A.
24
- B.
36
- C.
48
- D.
42
Attempted by 74 students.
Show answer & explanation
Correct answer: B
Solution: Let the tens digit be x and the ones digit be y, so the number is 10x + y.
When 27 is added the digits interchange, so
10x + y + 27 = 10y + x
Rearrange this equation to get
9x - 9y + 27 = 0, which simplifies to y - x = 3.
The problem statement implies the ones digit is twice the tens digit, so y = 2x.
Substitute y = 2x into y - x = 3:
2x - x = 3, so x = 3 and y = 6.
Therefore the number is 10x + y = 36. Check: 36 + 27 = 63, which is the digits reversed, so 36 satisfies the conditions.