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.
Find the difference between total male voters and total female voters in all the three villages?

Options

A. 400
B. 480
C. 440
D. 420

Answer

To solve the problem step by step, we will follow the information provided in the question carefully.

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

Let the number of voters in Vasantpur be \(27x\), in Govindpur be \(18x\), and in Vilashpur be \(25x\).

The equation can be set up as:
\[ 27x + 18x + 25x = 2800 \]
\[ 70x = 2800 \]
\[ x = \frac{2800}{70} = 40 \]

Now, we can find the number of voters in each village:
- Vasantpur: \(27x = 27 \times 40 = 1080\)
- Govindpur: \(18x = 18 \times 40 = 720\)
- Vilashpur: \(25x = 25 \times 40 = 1000\)

### Step 2: Determine the number of male voters in Vasantpur and Govindpur
The ratio of male voters in Vasantpur and Govindpur is given as 10:7. Let the number of male voters in Vasantpur be \(10y\) and in Govindpur be \(7y\).

The total number of voters in each village is known:
- Vasantpur: \(10y + \text{female voters in Vasantpur} = 1080\)
- Govindpur: \(7y + \text{female voters in Govindpur} = 720\)

### Step 3: Calculate the female voters in Govindpur
From Govindpur:
\[ \text{female voters in Govindpur} = 720 - 7y \]

### Step 4: Calculate the female voters in Vasantpur
According to the problem, the total female voters in Vasantpur are 60% more than those in Govindpur:
\[ \text{female voters in Vasantpur} = (720 - 7y) + 0.6(720 - 7y) = 1.6(720 - 7y) \]
Substituting this into the equation for Vasantpur:
\[ 10y + 1.6(720 - 7y) = 1080 \]
Expanding and simplifying:
\[ 10y + 1152 - 11.2y = 1080 \]
\[ -1.2y + 1152 = 1080 \]
\[ -1.2y = 1080 - 1152 \]
\[ -1.2y = -72 \]
\[ y = \frac{72}{1.2} = 60 \]

### Step 5: Calculate the number of male voters
Now substituting \(y\) back to find the number of male voters:
- Male voters in Vasantpur: \(10y = 10 \times 60 = 600\)
- Male voters in Govindpur: \(7y = 7 \times 60 = 420\)

### Step 6: Calculate the number of female voters in each village
Now we can find the female voters:
- Female voters in Govindpur: \(720 - 420 = 300\)
- Female voters in Vasantpur: \(1.6(720 - 420) = 1.6 \times 300 = 480\)

### Step 7: Determine male voters in Vilashpur
The problem states that the total male voters in Vilashpur are \(42\frac{6}{7}\%\) more than the male voters in Govindpur:
\[ \text{Male voters in Vilashpur} = 420 + \left(\frac{300}{7} \times 420\right) = 420 + 60 = 600 \]

### Step 8: Calculate female voters in Vilashpur
Total voters in Vilashpur: \(1000\)
\[ \text{Female voters in Vilashpur} = 1000 - 600 = 400 \]

### Step 9: Calculate total male and female voters
Now we can sum up the total male and female voters:
- Total male voters = \(600 + 420 + 600 = 1620\)
- Total female voters = \(480 + 300 + 400 = 1180\)

### Step 10: Find the difference between total male and female voters
\[ \text{Difference} = 1620 - 1180 = 440 \]

### Final Answer
The difference between total male voters and total female voters in all three villages is **440**.

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