Question

In an election, candidate A got \[75\% \] of the total valid votes. If \[15\% \] of the total votes were declared invalid and the total number of votes is \[560000\], find the number of valid votes polled in favour of the candidate.
A.$357000$
B.$280000$
C.$387500$
D.$355700$

Answer 1

Hint: First of all, we would write all the given information, then we would find the total number of valid votes with the help of which we would be able to find the number of votes polled in favour of candidate A easily (as it is given that A got \[75\% \] of the total valid votes).

Complete step-by-step answer:
According to the question, it is given that:
Total number of votes \[ = 560000\]
Now, votes can either be valid or invalid.
It is given that \[15\% \] of the total votes were declared invalid.
Hence, total number of invalid votes = \[15\% \] of \[560000\]
Now, we can write \[15\% \] as $\dfrac{{15}}{{100}}$
Hence, total number of invalid votes $ = \dfrac{{15}}{{100}} \times 560000$
Solving this further,
$ = 3 \times 28000$
$ = 84000$
Now, total number of valid votes $ = $ Total number of votes $ - $ Total number of invalid votes
\[ = 560000 - 84000\]
$ = 476000$
Now, we have to find the number of valid votes polled in favour of candidate A.
According to the question,
In an election, candidate A got \[75\% \] of the total valid votes.
As we know, total number of valid votes $ = 476000$
Hence, votes received by A in that election will be:
\[75\% \] of $476000$
As we know, we can write \[75\% \] as $\dfrac{{75}}{{100}}$
Hence, total votes received by A
$ = \dfrac{{75}}{{100}} \times 476000$
Solving further,
$ = 3 \times 119000$
$ = 357000$
Therefore, the number of valid vote polled in favour of candidate A$ = 357000$
Hence, option A is the correct answer.

Note: In order to answer this question we should know that the total number of votes which are polled can either be valid or invalid. And we consider those votes which are valid. Hence, while finding the total votes polled in favour of candidate A, we completely ignored the invalid votes and took only the valid votes into consideration. This is really important to solve these types of questions because if we would have taken a total number of votes instead of valid ones, then our answer would have become completely wrong.