Q. 5 A number consists of two digits. The sum of the digits is 9. If 45 is subtracted from the number,
its digits are interchanged. What is the number?
A two-digit number has a digit sum of 9. When 45 is subtracted from the number,
the digits of the number get interchanged. Find the number.
Correct Answer: 72
Problem Setup
Let the two-digit number be represented as:
10a + b, where:
- a = tens digit
- b = units digit
Given conditions:
a + b = 9 …(1)
After subtracting 45, digits reverse:
(10a + b) − 45 = 10b + a
Mathematical Solution
Simplify the equation:
10a + b − 45 = 10b + a
9a − 9b = 45
a − b = 5 …(2)
Now solve the system of equations:
a + b = 9
a − b = 5
Adding both equations:
2a = 14 → a = 7
Substitute a = 7:
b = 2
The required number = 72
Option Analysis
| Option | Number | Digit Sum | After Subtracting 45 | Digits Reversed? |
|---|---|---|---|---|
| (A) | 63 | 6 + 3 = 9 | 18 | No (Reverse = 36) |
| (B) | 72 | 7 + 2 = 9 | 27 | Yes |
| (C) | 81 | 8 + 1 = 9 | 36 | No (Reverse = 18) |
| (D) | 90 | 9 + 0 = 9 | 45 | No (Reverse = 09) |
Final Conclusion
Only 72 satisfies both conditions:
- Digits add up to 9
- Digits reverse after subtracting 45
Final Answer: 72
