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) 3260
 (B) 2700
 (C) 1290
 (D) 1600

Answer 1

$Hint -$ It can be solved by simple algebra. We can easily calculate the number of invalid votes from the given question. After this, we can calculate the number of valid votes that candidate A has got. Then by simple math, we can calculate the remaining valid votes that candidate B has got.

Complete step-by-step solution -
Total number of votes =7500
Now, 20% of the votes are invalid.
Calculating number of invalid votes $ \Rightarrow (20 * 7500)/100 = (20 * 75)$
$ = 1500$
Number of valid votes are (Total number of votes)-(Total invalid votes)
\[ \Rightarrow (7500) - (1500) = 6000{\text{ votes}}\]
Candidate A got 55% of the valid votes
Number of votes of candidate A $ \Rightarrow (55*6000)/100 = 55*60$
$ = 3300$
The number of valid votes that the other candidate got will be equal to
$
   \Rightarrow ({\text{Total valid votes) - (Valid votes of candidate A)}} \\
   \Rightarrow {\text{6000 - 3300 = 2700}} \\
$
$\therefore {\text{B is the correct option}}$
$Note-$ In these types of questions, we start off by calculating the number of all the individual entities. After calculating all the percentages, then we just have to do simple algebra to find out the correct answer. The main thing to accurately solve these types of questions is that we have to focus on the calculation of percentages.