1. Understand the Mathematical Property:
Let a two-digit number be represented as 10x+y, where x is the tens digit and y is the units digit. When the digits are reversed, the new number becomes 10y+x.
2. Formulate the Equation:
The problem states that the reversed number is 18 more than the original number.
Divide the entire equation by 9:
3. Find the Possible Pairs (x,y):
We need to find pairs of digits (x,y) where the difference is 2, keeping in mind that x (the tens digit) cannot be 0 for a two-digit number.
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If x=1, then y=3 (Number is 13 — this is the example given in the question)
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If x=2, then y=4 (Number is 24)
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If x=3, then y=5 (Number is 35)
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If x=4, then y=6 (Number is 46)
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If x=5, then y=7 (Number is 57)
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If x=6, then y=8 (Number is 68)
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If x=7, then y=9 (Number is 79)
4. Identify "Other" Numbers:
The question asks for other two-digit numbers besides 13.
The list of numbers found is: {13,24,35,46,57,68,79}.
Excluding 13, the other numbers are: {24,35,46,57,68,79}.
Total count of other numbers = 6.
Final Answer
The number of other two-digit numbers is 6.
Correct Option: (b)
