Aptitude - Percentage - Discussion

Total invalid votes = 20%.
Then valid votes = 80% out of which 55% for one candidate and 45% for the other candidate.
Total votes = 7500; Let that be the 100% votes.
So, 1% = 75.
80% = 6000.
6000 x 45/100 = 2700 (out of the total valid votes, the number of valid votes the other candidate got).

Votes got by other candidate is simply , 7500 * 4/5 * 9/20 = 2700 votes ..

Here;
7500 * 4/5 is the count of valid votes and 7500 * 4/5 * 9/20 is the votes got by another candidate.
Since the first candidate got 55% votes, the other got 45% votes which is 9/20.

7500 is the total vote.

And 20% are invalid hence, 1500 votes are invalid then 6000 is a valid vote and one gets 55% then another gets 45% of the valid vote it means 45% of 6000 so the answer becomes 2700.

So, here lets us consider total votes be 100%.
So, remove invalid votes i.e 20 per hen we get 80 per valid vote.
100%-20%(invalid votes) = 80%
Now in 80 per there are 55 per are valid votes so,
55/100x80 =55/10x8=11/2x8=11/1x4=44% we get for one candidate,

In question, they mention other person's valid votes so 80%(valid votes) - 44%(1st candidate) = 36(2nd candidate)
100% = 7500(they are given).
36% = x.
x = 7500 x 36/100 = 75x36 = 2700.
We get 2700 as final.

Number of invalid votes:

Total votes = 7500
% of invalid votes = 20
Number of invalid votes = 20/100 * 7500 = 1500


Number of valid votes:
Number of valid votes = 7500 - 1500 = 6000.


Votes won by the first candidate:
% of votes won by the first candidate = 55.
Number of votes won by the first candidate = 55/100 * 6000 = 3300.


Number of valid votes won by the other candidate:
Number of valid votes won by the other candidate = 6000 - 3300 = 2700.


Therefore, the number of valid votes that the other candidate got is 2700.

Thanks for your answer @Jabi Mir.

Easy solution is;.

(100-20)% of valid votes,
80/100*7500 = 6000,
45/100*6000 = 2700,
So, Ans= 2700 votes.

Percentage is always calculated sum of observation/no.of observation * 100%.

Total votes=7500 (that includes valid and invalid).

And given that 20% of votes are invalid.

So, 20%of 7500=1500 (invalid votes).

Now finding valid votes 7500 - 1500=6000.

The 1st person gained 55% of 6000 votes.
55%of 6000=3300 (1 person).

For other persons 6000 - 3300 = 2700 (2nd person).

Here first we have to understand the question clearly, it says total votes are 7500, out of which 20% of total votes are invalid, which means 80% is a valid vote. So find the total valid vote that is 80% of 7500 = 6000.

Now, we have 6000 valid votes. From 6000 valid votes, let's say candidate A has 55% valid vote according to the question given, which means candidate B has 45% valid vote so 45% of 6000 is 2700.