Rashi asked Aarush to take a two digit number and then reverse the digits. After that, she asked him to add the first number and the new number, then divide it by 11. She asked him to tell her the remainder. What will be the remainder?

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Solution

Let's take a two digit number 'ab'. Its general form is 10 × a + 1 × b. When we reverse the digits, the new number will be of the form 10 × b + 1 × a.

If we add both the numbers we get
(10 × a + 1 × b) + (10 × b + 1 × a)
=10a + b + 10b + a
= 11(a+b)

Hence, when divided by 11 it will not leave any remainder.

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