There are two candidates in an election. A candidate secured `40%` of total votes and defeated by the other candidate by 298 votes. Find total votes ?

Options

A. `1390`
B. `1190`
C. `1490`
D. `1690`

Answer

To solve the problem step by step, we will follow these calculations:

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

### Step 2: Calculate Votes Secured by Each Candidate
According to the problem, one candidate secured \( 40\% \) of the total votes. Therefore, the votes secured by this candidate (let's call them Candidate A) can be calculated as:
\[ \text{Votes for Candidate A} = 0.4V \]
The other candidate (let's call them Candidate B) secured the remaining votes, which is:
\[ \text{Votes for Candidate B} = V - 0.4V = 0.6V \]

### Step 3: Set Up the Equation Based on the Defeat
Candidate A was defeated by Candidate B by \( 298 \) votes. This means that the difference in votes between Candidate B and Candidate A is:
\[ \text{Votes for Candidate B} - \text{Votes for Candidate A} = 298 \]
Substituting the values we have:
\[ 0.6V - 0.4V = 298 \]

### Step 4: Simplify the Equation
Now, simplify the left-hand side:
\[ 0.2V = 298 \]

### Step 5: Solve for Total Votes
To find \( V \), divide both sides by \( 0.2 \):
\[ V = \frac{298}{0.2} = 1490 \]

Thus, the total number of votes is:
\[ \text{Total Votes} = 1490 \]

### Summary of the Solution
The total number of votes in the election is \( 1490 \).

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