Question

A number is multiplied by 5 and 25 is added to it. The result is divided by 5 and the original number is subtracted from the quotient. What will be the remainder?
A. 19
B. 3
C. 5
D. 28

Answer 1

Hint: We will, first of all, assume the starting number to be ‘x’. Then, multiply it by 5 and add 25 to it. Then divide the resultant by 5 and calculate the quotient whatever it is. Now, we will subtract ‘x’ from the quotient and see what we get.

Complete step-by-step solution:
Let the original number we initially are given to be ‘x’.
Now, we need to multiply it by 5 as mentioned in question.
\[ \Rightarrow \] We will now get $5 \times x$ that is 5x.
Now, we need to add 25 to it according to the question.
\[ \Rightarrow \] We will now get 5x + 25.
We can rewrite this as 5 (x + 5).
Now, we need to divide this by 5 as mentioned in the second line of the question.
\[ \Rightarrow \] We will now get $\dfrac{{5(x + 5)}}{5}$ which is definitely equal to x + 5.
Now, we need to subtract the original number from it as mentioned in the second line of the question.
\[ \Rightarrow \] We will now get (x + 5) – (x) = x + 5 - x = 5.
Hence, the final required answer is ‘5’.

$\therefore $ The correct option is (C).

Note: The students must note that you need to do steps in the same sequence as given in the question to obtain the correct answer without any chaos.
The students must note that it works like this because eventually we have to find the difference, otherwise the solution or answer would have included ‘x’ in it.
The alternate way to do the same is doing it briefly in a single step. This means, we can do all the required in a single step to get to our answer like as follow:
Alternate way:-
$ \Rightarrow $Remainder = $\dfrac{{5 \times x + 25}}{5} - x$
$ \Rightarrow $Remainder = $\dfrac{{5x + 25}}{5} - x$
$ \Rightarrow $Remainder = $\dfrac{{5(x + 5)}}{5} - x$
$ \Rightarrow $Remainder = $x + 5 - x$
$ \Rightarrow $Remainder = 5
Hence, the final required answer is ‘5’.
$\therefore $ the correct option required is (C).