in an election contested by two candidates a and b only 80% of the registered voters cast their votes.among the votes polled only 90% of them were valid. a got 35% of the valid votes and lost by a margin of 5454 votes.find the number of registered voters.

Let's break down the problem step by step.

1. **Let the total number of registered voters be \( N \).**

2. **80% of the registered voters cast their votes, so the number of votes cast is:**
   \[
   \text{Votes cast} = 0.8N
   \]

3. **Among the votes cast, only 90% were valid, so the number of valid votes is:**
   \[
   \text{Valid votes} = 0.9 \times 0.8N = 0.72N
   \]

4. **Candidate A received 35% of the valid votes, so the number of votes candidate A received is:**
   \[
   \text{Votes for A} = 0.35 \times 0.72N = 0.252N
   \]

5. **Let the number of votes candidate B received be \( V_B \). Since A lost by a margin of 5454 votes:**
   \[
   V_B = 0.252N + 5454
   \]

6. **Since the total number of valid votes is shared between A and B:**
   \[
   V_B + \text{Votes for A} = 0.72N
   \]
   Substituting \( V_B \) from the previous equation:
   \[
   0.252N + 5454 + 0.252N = 0.72N
   \]
   Simplifying the equation:
   \[
   0.504N + 5454 = 0.72N
   \]
   \[
   0.216N = 5454
   \]

7. **Solving for \( N \):**
   \[
   N = \frac{5454}{0.216} = 25250
   \]

So, the total number of registered voters is **25,250**.

Would you like further details on this solution, or do you have any questions?

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Here are 5 questions related to this problem:

1. How would the result change if only 70% of the registered voters cast their votes?
2. What would happen if the margin of loss was increased to 10,000 votes?
3. How would the result be affected if candidate A received 50% of the valid votes?
4. What if 95% of the votes cast were valid instead of 90%?
5. How would you calculate the number of invalid votes in this election?

**Tip:** When solving problems involving percentages, it's often easier to express each step as an equation before plugging in numbers.

Learn how to solve the problem of calculating the number of registered voters in an election where candidate A lost by 5454 votes. Includes step-by-step calculations involving percentages, valid votes, and candidate vote shares.

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