Question

In an election between two candidates, the first candidate gets 80% of the total valid votes. If 10% of the total 1, 80, 000 votes were declared invalid then the number of valid votes polled in favour of the second candidate are:
A. 31400
B. 31500
C. 32400
D. 32420

Answer 1

Hint: Given, 10% of the total 1, 80, 000 votes were declared invalid. Therefore, find the number of valid votes i.e. 90% of 1, 80, 000. Now, of these valid votes, 80% was in favour of the first candidate. So the rest of the valid votes were polled in favour of the second candidate.

Complete step-by-step solution:
Given that, 10% of the total 1, 80, 000 votes were declared invalid.
Therefore, the number of valid votes are = 90% of the total votes.
$\Rightarrow$number of valid votes $ = 180000 \times \dfrac{{90}}{{100}}$
$ = 18000 \times 9$
$ = 162000$
Now, given that the first candidate gets 80% of the total valid votes.
Therefore total votes polled in favour of the first candidate is
$ = 162000 \times \dfrac{{80}}{{100}}$
$ = 129600$
Hence, number of votes polled in favour of the second candidate is
= total number of valid votes – number of votes polled in favour of the first candidate
$ = 162000 - 129600$
$ = 32400$
So, the required number of votes polled in favour of the second candidate is 32400.

Therefore, the correct answer is option (C).

Note: First find the number of valid votes i.e. 90% of 1, 80, 000. Now, of these valid votes, 80% was in favour of the first candidate. So 20% of the valid votes were polled in favour of the second candidate.