A number consists of two digits. The sum of the digits is 9. If 63 is…
2022
A number consists of two digits. The sum of the digits is 9. If 63 is subtracted from the number, its digits are interchanged. Find the number.
Answer: C. 81 — For any two-digit number with tens digit a and units digit b, the number equals 10a + b, and interchanging the digits gives 10b + a. Subtracting the reversed…
- A.
72
- B.
90
- C.
81
- D.
None of these
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Correct answer: C
For any two-digit number with tens digit a and units digit b, the number equals 10a + b, and interchanging the digits gives 10b + a. Subtracting the reversed number from the original number always yields 9(a − b) — a direct consequence of place value — which converts a digit-interchange condition into a simple linear equation.
Let the tens digit be a and the units digit be b, so the number is 10a + b.
The digit-sum condition gives the first equation: a + b = 9.
Subtracting 63 from the number interchanges its digits, so (10a + b) − 63 = 10b + a.
Simplifying the second equation: 9a − 9b = 63, which gives a − b = 7.
Adding a + b = 9 and a − b = 7 gives 2a = 16, so a = 8 and b = 1.
The number is 10a + b = 10(8) + 1 = 81.
Cross-check: 81 − 63 = 18, and 18 is exactly 81 with its digits swapped, confirming both the digit-sum and interchange conditions.