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The sum of the digits of a two-digit number is 9. If 27 is subtracted from the number, its digits are interchanged. Which of these is the product of the digits of the number?Read more on Sarthaks.com - https://www.sarthaks.com/2037753/the-sum-the-digits-two-digit-number-subtracted-from-the-number-its-digits-are-interchanged?
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The sum of the digits of a two-digit number is 9. If 27 is subtracted ...
Given Information:
The sum of the digits of a two-digit number is 9. When 27 is subtracted from the number, its digits are interchanged.

Let's solve step by step:
1. Let the two-digit number be represented as 10x + y:
- x represents the digit in the tens place
- y represents the digit in the ones place
2. According to the given information:
- x + y = 9 (Sum of the digits is 9)
- 10x + y - 27 = 10y + x (When 27 is subtracted, digits are interchanged)
3. Solving the equations simultaneously:
- From x + y = 9, we get x = 9 - y
- Substituting x in the second equation:
10(9 - y) + y - 27 = 10y + 9 - y
90 - 10y + y - 27 = 10y + 9 - y
90 - 9y - 27 = 9y + 9
63 = 18y
y = 63/18
y = 3
4. Calculating x using x = 9 - y:
- x = 9 - 3
- x = 6
5. Therefore, the two-digit number is 63:
- Product of the digits (3 * 6) = 18

Conclusion:
The product of the digits of the two-digit number is 18.
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The sum of the digits of a two-digit number is 9. If 27 is subtracted from the number, its digits are interchanged. Which of these is the product of the digits of the number?Read more on Sarthaks.com - https://www.sarthaks.com/2037753/the-sum-the-digits-two-digit-number-subtracted-from-the-number-its-digits-are-interchanged?
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