After the division of a number successively by 3, 4 and 7, the remainder obtained is 2, 1 and 4 respectively. What will be remainder if 84 divide the same number?

Explanation:-

As the Number gives a remainder of 4 when it is divided by 7, then the number must be in form of (7x +4).

The same gives remainder 1 when it is divided 4, so the number must be in the form of {4*(7x+4)+1}.

Also, the number when divided by 3 gives remainder 2, thus number must be in form of [3*{4*(7x +4)+1}+2]

Now, On simplifying,
[3*{4*(7x+4)+1}+2]
= 84x+53.
We get the final number 53 more than a multiple of 84. Hence, if the number is divided by 84,
the remainder will be 53.