The difference between a two-digit number by interchanging the digits is 27. What is the difference between the two digits of the number?

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answer is C.

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Detailed Solution

According to the question, we are given a two-digit number and its difference with the number obtained by interchanging the digits is 27.
First of all, let us assume that the unit place and tenth place of the required number is x and y respectively.
Our number will look like,

Since the place value of x and y is unit and tenth place so, the above number must be equal to,
10y + x.
The original number = 10y + x…………………….(1)
After interchanging the digits, our number will look like,

Here, we can observe that the place value of x and y is tenth and unit place so, the above number must be equal to, 10x + y.
The number after the interchange of digits = 10x + y………………(2)
We are also given one more information that is the difference between the original number and the number obtained by interchanging the digits is 27…………….(3)
Using equation (3) and subtracting equation (2) from equation (1), we get
⇒ (10y + x) − (10x + y) = 27
⇒10y + x − 10x – y = 27
⇒ 9y − 9x = 27
⇒9(y − x) = 27
⇒ (y − x) =

279

⇒ (y – x) = 3………………………….(4)
Earlier, we have assumed that x and y are the unit and tenth place digit of the original number.
In equation (4), (y − x) means the difference between the digits of the number.
Therefore, the difference between the digits is 3.

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