In an election contested by two candidates ,one candidate got 30% of total votes and still lost by 500 votes, then find the total number of votes casted.

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Define the total number of votes
Let the total number of votes be represented as \( x \).

### Step 2: Calculate the votes received by the first candidate
The first candidate received 30% of the total votes. Therefore, the votes received by the first candidate can be calculated as:
\[ \text{Votes for Candidate 1} = 30\% \text{ of } x = \frac{30}{100} \times x = 0.3x \]

### Step 3: Calculate the votes received by the second candidate
Since there are only two candidates, the votes received by the second candidate can be calculated as:
\[ \text{Votes for Candidate 2} = x - \text{Votes for Candidate 1} = x - 0.3x = 0.7x \]

### Step 4: Set up the equation based on the information given
According to the problem, the first candidate lost by 500 votes. This can be expressed as:
\[ \text{Votes for Candidate 2} - \text{Votes for Candidate 1} = 500 \]
Substituting the values we calculated:
\[ 0.7x - 0.3x = 500 \]

### Step 5: Simplify the equation
Now simplify the left side:
\[ 0.4x = 500 \]

### Step 6: Solve for \( x \)
To find the total number of votes, divide both sides by 0.4:
\[ x = \frac{500}{0.4} = 1250 \]

### Conclusion
The total number of votes casted in the election is \( 1250 \).

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