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 :​

Answer 1

Answer:

• Total Votes = 7500
• Valid Votes = (100 - 20)% = 80%
• 1st Candidate Got = 55%

• Number of valid votes 2nd candidate got :

$:\implies\sf Votes_{2nd\:Candidate}=Total \times Valid\% \times Got\%\\\\\\:\implies\sf Votes_{2nd\:Candidate} = 7500 \times 80\% \times (100 - 55)\%\\\\\\:\implies\sf Votes_{2nd\:Candidate} = 7500 \times \dfrac{80}{100} \times\dfrac{45}{100}\\\\\\:\implies\sf Votes_{2nd\:Candidate} = 75\times \dfrac{4}{5} \times 45\\\\\\:\implies\sf Votes_{2nd\:Candidate} = 300 \times 9\\\\\\:\implies\underline{\boxed{\sf Votes_{2nd\:Candidate} = 2700}}$

⠀

$\therefore\:\underline{\textsf{Other candidate got \textbf{2700} valid votes}}.$

Answer 2

Given:

• First candidate be x

• Second candidate be y

• Total votes = 7500

___________________

Solution :

(A) Percentage of valid votes for x = 55%

(B) Percentage of total invalid vote = 20%

Now I noted that percentage of valid votes = (100-20)% = 80%

Now,

Remain percentage for y = (100 - 55) % = 45%

Now the total votes are 7500

Total valid and invalid for y are :

$y = 7500\times\frac{45}{100}\\ y = 75\times45\\y= 3,375$

Total valid vote % = 7500×80% = 6000

Total valid votes of x = 6000×55% = 3,300

Total valid vote for candidate y

=> 6000 -3300 = 2,700

$\large{\bold{\underline{y = 2,700\:votes}}}$