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Candidate A, B and C are contesting elections. Each voter can only vote for a single candidate. \(20\)% of the voters refrained from voting and candidates A, B and C received votes in the ratio \(4 :3: 1\) respectively. If there were no invalid votes and Candidate C got \(2\) million votes, then how many voters (in millions) refrained from voting?


    A. \(2\)
    B. \(2.4\)
    C. \(3.2\)
    D. \(4\)
    E. \(8\)


Let , Total Voters be 100
No of Voters who didn't cast their votes is 20
No of Voters who casted their votes is 80

Voters received by A:B:C = 40 : 30 : 10

It is 10 represents 2 million people
So, 1 represents 2/10 million people
And 100 represents 2/10*100 = 20million people

Voters who didn't cast their votes is 20% of 20 million people = 4 million people...

Answer will hence be (D) 4 million..
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Hey,

PFB the official solution.

Working Out:

    • Let the total number of votes = T
    • As 20% of the total voters refrained from voting,
      o 100% -20% = 80% of voters voted
      o Therefore, the total number of people who voted = 80% of T = 0.8 x T
    • Candidates A, B and C received votes in the ratio 4 :3: 1 respectively means
      o Number of votes received by Candidate A = 4X
      o Number of votes received by Candidate B = 3X
      o Number of votes received by Candidate C = 1X

Drawing the tree structure, we get



From the tree structure,

    • People who voted = 0.8T = 4X + 3X + 1X
    • 0.8T = 8X = 8 x 2 million
    • 0.8T = 16 million
    T = 20 million

People who refrained from voting
    • 0.2T
    • 0.2 x 20 million
    4 million

Correct Answer: Option D

Thanks,
Saquib
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