In an election between two candidates, the winning candidate got 70% of the valid votes and won by a majority of 9000 votes.If out of total votes polled 90% votes are valld, what is the total number of votes polled?

Options

A. 30000
B. 25000
C. 22500
D. 27000

Answer

To solve the problem step by step, we will follow the reasoning laid out in the video transcript.

### Step 1: Understand the Votes Distribution
In the election, the winning candidate received 70% of the valid votes. Therefore, the losing candidate received the remaining 30% of the valid votes.

### Step 2: Define the Majority
The majority by which the winning candidate won is given as 9000 votes. This majority represents the difference between the votes received by the winning candidate and the losing candidate.

### Step 3: Set Up the Equation
Let the total number of valid votes be \( V \).

- Votes received by the winning candidate = \( 0.7V \)
- Votes received by the losing candidate = \( 0.3V \)

The difference (majority) between the two candidates' votes can be expressed as:
\[ 0.7V - 0.3V = 9000 \]
This simplifies to:
\[ 0.4V = 9000 \]

### Step 4: Solve for Valid Votes
To find \( V \), divide both sides of the equation by 0.4:
\[ V = \frac{9000}{0.4} = 22500 \]

### Step 5: Calculate Total Votes Polled
We know that 90% of the total votes polled are valid. Let the total number of votes polled be \( T \).

Since 90% of \( T \) equals the valid votes \( V \):
\[ 0.9T = 22500 \]

### Step 6: Solve for Total Votes Polled
Now, divide both sides by 0.9 to find \( T \):
\[ T = \frac{22500}{0.9} = 25000 \]

### Conclusion
The total number of votes polled is **25000**.

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