Question
A two-digit number has a sum of its digits equal to 9.
Additionally, if 27 is subtracted from this number, the resulting number has its digits reversed. What is the original number?Solution
ATQ,
Let the two-digit number be 10a + b. Given: a + b = 9 Also, subtracting 27 reverses the digits: 10a + b - 27 = 10b + a So, 9a - 9b = 27 a - b = 3 Now solve: a + b = 9 a - b = 3 Add both equations: 2a = 12 a = 6 Then, b = 3 So the original number is 63. Check: 63 - 27 = 36 Answer: 63
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