In a student council election, there were three contestants. All the voters participated in the voting and 10% of votes were declared invalid. The contestants got the votes in the ratio 8 : 7 : 5. If the second candidate in the list got 4725 votes, the total number of valid votes is:
- ((a))
10,000
- ((b))
11,500
- ((c))
13,500
- ((d))
9,000
Show Answer
13,500

Shortcut Trick
The valid votes are distributed among the three candidates in the ratio 8 : 7 : 5.
Total ratio parts = 8 + 7 + 5 = 20 parts.
The second candidate's share is 7 parts, which is given as 4725 votes.
Value of 1 part = 4725 ÷ 7 = 675 votes.
Total valid votes = 20 parts × 675 = 13500.
∴ The correct answer is 13,500.

Alternate Method
Given:
Ratio of votes received by the three contestants = 8 : 7 : 5
Votes received by the second candidate = 4725
10% of total votes were declared invalid (Note: This is extraneous data since we only need the total valid votes).
8 Parts Candidate 1
7 Parts Candidate 2 4725 Votes
5 Parts Candidate 3
Total Valid Votes = 20 Parts
Calculations:
Let the number of valid votes obtained by the three candidates be 8x, 7x, and 5x respectively.
⇒ Votes of the second candidate = 7x
⇒ 7x = 4725
⇒ x = 4725 ÷ 7
⇒ x = 675
The total number of valid votes is the sum of votes received by all candidates.
⇒ Total valid votes = 8x + 7x + 5x
⇒ Total valid votes = 20x
⇒ Total valid votes = 20 × 675
⇒ Total valid votes = 13500
∴ The correct answer is 13,500.

Additional Information
Ratio Distribution
When a quantity is divided into a ratio a : b : c, the total quantity corresponds to the sum of the ratio parts (a + b + c).
Valid vs Invalid Votes
Total votes cast = Valid votes + Invalid votes. Invalid votes are removed from the pool before calculating the individual shares of candidates.
Extraneous Information
Examiners often include extra data (like the 10% invalid votes in this problem) that is not required to find the final value, testing the candidate's ability to extract only relevant data.





















































