Question
Download Solution PDFA two digit number is such that the sum of the digits is 9. When the number with the same digits are reversed is subtracted from the original number, the difference is 27. What is the original number?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Sum of the digits of a two-digit number = 9
Original number - Reversed number = 27
Formula used:
A two-digit number can be represented as 10x + y, where x is the tens digit and y is the units digit.
Calculations:
Let the original number be 10x + y
The sum of the digits: x + y = 9 --- (1)
The number with digits reversed will be 10y + x
When the reversed number is subtracted from the original number, the difference is 27:
(10x + y) - (10y + x) = 27
10x + y - 10y - x = 27
9x - 9y = 27
x - y = 3 --- (2)
Add equation (1) and (2):
(x + y) + (x - y) = 9 + 3
2x = 12
⇒ x = 6
Substitute x = 6 into equation (1):
6 + y = 9
⇒ y = 3
The original number = 10x + y = 10(6) + 3 = 60 + 3 = 63
∴ The correct answer is option 4.
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