In an election between two candidates, the winning candidate has got `70%` of the votes polled and has won by `15400` votes. What is he number of votes polled for loosing candidate ?

Options

A. `38500`
B. `11550`
C. `26950`
D. `13550`

Answer

To find the number of votes polled for the losing candidate, we can follow these steps:

### Step 1: Understand the percentages
In this election, the winning candidate received 70% of the votes, while the losing candidate received 30% of the votes.

### Step 2: Set up the equation
Let the total number of votes polled be \( V \). According to the problem:
- Votes for the winning candidate = \( 0.7V \)
- Votes for the losing candidate = \( 0.3V \)

### Step 3: Determine the difference in votes
The difference between the votes received by the winning candidate and the losing candidate is given as 15,400 votes. Therefore, we can write the equation:
\[ 0.7V - 0.3V = 15400 \]

### Step 4: Simplify the equation
Combine like terms:
\[ 0.4V = 15400 \]

### Step 5: Solve for \( V \)
To find the total votes polled, divide both sides by 0.4:
\[ V = \frac{15400}{0.4} \]
Calculating this gives:
\[ V = 38500 \]

### Step 6: Calculate votes for the losing candidate
Now, we can find the number of votes for the losing candidate:
\[ \text{Votes for losing candidate} = 0.3V = 0.3 \times 38500 \]
Calculating this gives:
\[ \text{Votes for losing candidate} = 11550 \]

### Final Answer
The number of votes polled for the losing candidate is **11,550**.

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