किसी चुनाव में 8% मतदाताओं ने अपने मत नहीं डाले। इस चुनाव में केवल दो ही प्रत्याशी थे। जिन्होंने वाले प्रत्याशी ने कुल मतों के 48% मत प्राप्त कर 1100 मतों से चुनाव में दूसरे प्रत्य... किसी चुनाव में 8% मतदाताओं ने अपने मत नहीं डाले। इस चुनाव में केवल दो ही प्रत्याशी थे। जिन्होंने वाले प्रत्याशी ने कुल मतों के 48% मत प्राप्त कर 1100 मतों से चुनाव में दूसरे प्रत्याशी को हरा दिया। चुनाव में कुल मत कितने थे? Read more

Steps to Solve

1. Define total votes and voting percentage Let the total votes be denoted as $T$. Given that 8% of the voters did not vote, the percentage of voters who did vote is 92%, which can be expressed as (0.92T).

2. Calculate votes for the winning candidate The winning candidate received 48% of the total votes. Therefore, the votes received by the winning candidate can be calculated as: $$ \text{Votes by winning candidate} = 0.48T $$

3. Set up the equation for the margin of victory The winning candidate won by 1100 votes. This means the losing candidate received: $$ \text{Votes by losing candidate} = \text{Votes by winning candidate} - 1100 = 0.48T - 1100 $$

4. Relate the votes of the losing candidate to total votes Since there are only two candidates, the votes of the losing candidate can also be calculated as 52% of the total votes: $$ \text{Votes by losing candidate} = 0.52T $$

5. Set up the equation Setting the two expressions for the losing candidate's votes equal: $$ 0.48T - 1100 = 0.52T $$

6. Solve for T Rearranging the equation gives: $$ 1100 = 0.52T - 0.48T $$ $$ 1100 = 0.04T $$ Now, divding both sides by 0.04: $$ T = \frac{1100}{0.04} = 27500 $$