Read the data carefully and answer the following questions:
Total 2800 voters in the three villages, i.e. Vasantpur, Govindpur and Vilashpur. Ratio of total voters in Vasantpur, Govindpur and Vilashpur is 27 : 18 : 25 respectively. Ratio of male voters in Vasantpur and Govindpur 10: 7 and total female voters in Vasantpur are 60% more than total female voters in Govindpur. Total male voters in Vilashpur are `42(6)/(7)%` more than total male voters in Govindpur.
Total male voters in Vasantpur are what percent more than total female voters in Vilashpur?

Options

A. `50%`
B. `60%`
C. `55%`
D. `45%`

Answer

To solve the problem step by step, we will break down the information provided and calculate the required values.

### Step 1: Determine the number of voters in each village
The total number of voters is 2800, and the ratio of voters in Vasantpur, Govindpur, and Vilashpur is given as 27:18:25.

Let the common multiplier be \( A \). Then, the number of voters in each village can be expressed as:
- Vasantpur = \( 27A \)
- Govindpur = \( 18A \)
- Vilashpur = \( 25A \)

The equation for total voters is:
\[ 27A + 18A + 25A = 2800 \]
\[ 70A = 2800 \]
\[ A = \frac{2800}{70} = 40 \]

Now, substituting \( A \) back to find the number of voters in each village:
- Vasantpur = \( 27 \times 40 = 1080 \)
- Govindpur = \( 18 \times 40 = 720 \)
- Vilashpur = \( 25 \times 40 = 1000 \)

### Step 2: Determine the number of male voters in Vasantpur and Govindpur
The ratio of male voters in Vasantpur to Govindpur is given as 10:7.

Let the number of male voters in Vasantpur be \( 10X \) and in Govindpur be \( 7X \).

The total number of voters in each village gives us:
\[ 10X + \text{female voters in Vasantpur} = 1080 \]
\[ 7X + \text{female voters in Govindpur} = 720 \]

### Step 3: Calculate female voters in Govindpur
Let the number of female voters in Govindpur be \( F_g \).
Then,
\[ F_g = 720 - 7X \]

### Step 4: Calculate female voters in Vasantpur
The problem states that the total female voters in Vasantpur are 60% more than those in Govindpur:
\[ \text{Female voters in Vasantpur} = F_g + 0.6F_g = 1.6F_g \]
Substituting \( F_g \):
\[ \text{Female voters in Vasantpur} = 1.6(720 - 7X) \]

### Step 5: Set up the equation
Now we can set up the equation:
\[ 1080 - 10X = 1.6(720 - 7X) \]
Expanding and simplifying:
\[ 1080 - 10X = 1152 - 11.2X \]
Rearranging gives:
\[ 1.2X = 72 \implies X = 60 \]

### Step 6: Calculate the number of male voters
Now substituting \( X \) back:
- Male voters in Vasantpur = \( 10X = 10 \times 60 = 600 \)
- Male voters in Govindpur = \( 7X = 7 \times 60 = 420 \)

### Step 7: Calculate female voters in each village
Now, we can find the female voters:
- Female voters in Govindpur = \( 720 - 420 = 300 \)
- Female voters in Vasantpur = \( 1080 - 600 = 480 \)

### Step 8: Determine male voters in Vilashpur
The problem states that male voters in Vilashpur are \( 42\frac{6}{7}\% \) more than those in Govindpur:
\[ \text{Male voters in Vilashpur} = 420 + \left(\frac{300}{7} \times 42\right) = 420 + 180 = 600 \]

### Step 9: Calculate female voters in Vilashpur
Total voters in Vilashpur = 1000, so:
\[ \text{Female voters in Vilashpur} = 1000 - 600 = 400 \]

### Step 10: Calculate the percentage of male voters in Vasantpur compared to female voters in Vilashpur
Now, we need to find out what percent more the total male voters in Vasantpur are than the total female voters in Vilashpur:
\[ \text{Percentage} = \left(\frac{\text{Male voters in Vasantpur} - \text{Female voters in Vilashpur}}{\text{Female voters in Vilashpur}}\right) \times 100 \]
Substituting the values:
\[ \text{Percentage} = \left(\frac{600 - 400}{400}\right) \times 100 = \left(\frac{200}{400}\right) \times 100 = 50\% \]

### Final Answer
Total male voters in Vasantpur are **50% more** than total female voters in Vilashpur.

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