The difference between a 2-digit number and the number obtained by interchanging the digits is . What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is ?
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Determine the difference between the sum and the difference of digits of the number.
Explanation of the correct option:
B. Assume that the number is .
The number after interchanging its digits is .
The difference between the digits is .
Simplify the expression of the difference of numbers:
The ratio of the digits is .
Since , .
This implies that .
Substitute into and solve:
So, .
The sum of the digits is .
The difference of the digits is .
So, the difference between the sum and the difference of the digits of the number is .
Thus, option (B) is correct.
Explanation of the incorrect options.
Since the difference between the sum and the difference of the digits of the number is , so options (A), (C), and (D) are incorrect.
Hence,option (B) is correct.