The sum of the digits of a two-digit number is 9. If 27 is added to the…
2016
The sum of the digits of a two-digit number is 9. If 27 is added to the number, the digits interchange their places. Find the number.
Answer: A. 36 — Let the two-digit number be 10x + y, where x is the tens digit and y is the units digit. Given that the sum of the digits is 9, so x + y = 9. Adding 27…
- A.
36
- B.
45
- C.
63
- D.
72
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Correct answer: A
Let the two-digit number be 10x + y, where x is the tens digit and y is the units digit.
Given that the sum of the digits is 9, so x + y = 9.
Adding 27 reverses the digits, so the new number is 10y + x, and we have 10y + x = 10x + y + 27.
Rearrange that equation: 9y - 9x = 27, which simplifies to y - x = 3.
Now solve the system of equations:
x + y = 9
y - x = 3
Add the two equations: 2y = 12, so y = 6.
Then x = 9 - y = 3. Therefore the number is 10x + y = 36.
Verification: 3 + 6 = 9 and 36 + 27 = 63, which is the reversal of 36. So the answer 36 is correct.