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What will be the two-digit number whose sum of digits is 11 and it is 9 less than the number obtained by interchanging the digits?

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answer is C.

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Detailed Solution

We have to find the two-digit number.
To be interchangeable, the number must be two digits or greater. Reverse the given number if it has two digits.
Suppose x is the number's unit digit.
Then, the ten's digit:

⇒ 11 − x

Thus, the number is:

= 10 11 − x + x

= 110 − 10 x + x

= 110 − 9 x

When the digits are interchanged, then unit digit:

= 11 − x

And, tens digit:

= x

So, the number after interchanging the digits:

= 10 x + (11 − x) = 9 x + 11

According to the question-

9 x + 11 − (110 − 9 x) = 9 ⇒ 9 x + 11 − 110 + 9 x = 9 ⇒ 18 x = 110 − 2 ⇒ 18 x = 108 ⇒ x = 10818 ⇒ x = 6

Thus, the unit digit is 6.
And, the tenth digit is:

= 11 − x = 11 − 6 = 5

So, it can be concluded that the number is 56.
Therefore, option 3 is correct.

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