Question

In an election between two candidates, one got 55% of the total valid votes. 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was
(a)2700
(b)2900
(c)3000
(d)3200

Answer 1

Hint: First we have to calculate invalid votes by using the given percent and then subtract it from the total number of votes. Then we have to calculate the total number of votes of the first candidate. After that we have to subtract the number of votes of the first candidate from the total number of votes, to get the number of valid votes the other candidate successfully got.

Complete step-by-step answer:
Total number of votes (both valid and invalid) in the election = 7500.
Number of invalid casted is 20 percent of the total number of votes in the election.
So, number of invalid votes = $\dfrac{20}{100}\times 7500$
Number of invalid votes = $1500.$
Total number of valid votes = $7500-1500=6000$.
Total number of votes of the first candidate is 55 percent of valid votes casted in the election.
So, the number of votes of first candidate =$\dfrac{55}{100}\times 6000$
The number of votes of first candidate$=3300.$
Now, calculating the total number of votes of other candidates as Total number of votes – number of votes of first candidate.
Total number of votes of other candidate = 6000 – 3300
Total number of votes of other candidates = 2700.
$\therefore $The total number of votes of the second candidate is 2700.
So, amongst the given options option (a) is correct.

Note: We must first separate the false votes from total votes to evaluate the valid votes of any candidate. If a student first evaluates the valid votes without subtracting the invalid votes then a big blunder has been committed by the student.