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In a college election between two students, 10% of the votes cast are invalid. The winner gets 70% of the valid votes and defeats the loser by 1800 votes. How many votes were totally cast?Options1,8005,0003,6007,200

Question

In a college election between two students, 10% of the votes cast are invalid. The winner gets 70% of the valid votes and defeats the loser by 1800 votes. How many votes were totally cast?Options1,8005,0003,6007,200

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Solution

Let's solve this step by step:

  1. Let's assume the total number of votes cast is X.

  2. According to the problem, 10% of the votes cast are invalid. So, the number of valid votes is 90% of X, which is 0.9X.

  3. The winner gets 70% of the valid votes, which is 0.7 * 0.9X = 0.63X.

  4. The loser gets the remaining valid votes, which is 0.9X - 0.63X = 0.27X.

  5. The winner defeats the loser by 1800 votes. So, 0.63X - 0.27X = 1800 votes.

  6. Solving the above equation, we get 0.36X = 1800.

  7. Therefore, the total number of votes cast, X = 1800 / 0.36 = 5000 votes.

So, the total number of votes cast is 5000.

This problem has been solved

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