In a student council election, five candidates contested for a single position. 75% of the students enrolled in the institution voted. One candidate secured 20% of the votes polled, while the votes obtained by the remaining four candidates were in the ratio $2:3:4:6$. The candidate with the highest votes got 120 votes more than the candidate with the second-highest votes. What is the total number of students enrolled in the institution?
Answer and solution
Correct answer: B
Solution
Let votes polled $= V$. The other four share $80\%$ of $V$ in the ratio $2:3:4:6$ (total 15).
Highest $= 80\% \times \tfrac{6}{15} = 32\%$ of $V$; second-highest $= 80\% \times \tfrac{4}{15} = \tfrac{64}{3}\%$ of $V$
Difference $= \tfrac{32}{3}\%$ of $V = 120 \Rightarrow V = 1125$
$75\%$ of enrolled $= 1125 \Rightarrow$ enrolled $= 1500$
Highest $= 80\% \times \tfrac{6}{15} = 32\%$ of $V$; second-highest $= 80\% \times \tfrac{4}{15} = \tfrac{64}{3}\%$ of $V$
Difference $= \tfrac{32}{3}\%$ of $V = 120 \Rightarrow V = 1125$
$75\%$ of enrolled $= 1125 \Rightarrow$ enrolled $= 1500$