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 ratio of male voters in Govindpur to female voters Vasantpur ?

Options

A. `6:7`
B. `7:9`
C. `7:10`
D. `7:8`

Answer

To solve the problem step by step, we will follow the information provided in the question and the video transcript.

### 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 common multiple be \( A \). Therefore, we can express the number of voters in each village as:
- Vasantpur = \( 27A \)
- Govindpur = \( 18A \)
- Vilashpur = \( 25A \)

The total can be expressed as:
\[ 27A + 18A + 25A = 2800 \]
\[ 70A = 2800 \]
\[ A = \frac{2800}{70} = 40 \]

Now we can 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 and female voters in Govindpur
The ratio of male voters in Vasantpur and Govindpur is given as 10:7. Let the number of male voters in Govindpur be \( 7X \) and in Vasantpur be \( 10X \).

From the total number of voters in Govindpur:
\[ 7X + \text{Female voters in Govindpur} = 720 \]
Let the female voters in Govindpur be \( Y \). Thus:
\[ Y = 720 - 7X \]

### Step 3: Determine the number of female voters in Vasantpur
It is given that the total female voters in Vasantpur are 60% more than the total female voters in Govindpur. This can be expressed as:
\[ \text{Female voters in Vasantpur} = Y + 0.6Y = 1.6Y \]

Substituting for \( Y \):
\[ \text{Female voters in Vasantpur} = 1.6(720 - 7X) \]

The total number of voters in Vasantpur is:
\[ \text{Male voters in Vasantpur} + \text{Female voters in Vasantpur} = 1080 \]
\[ 10X + 1.6(720 - 7X) = 1080 \]

### Step 4: Solve for \( X \)
Expanding the equation:
\[ 10X + 1152 - 11.2X = 1080 \]
Combining like terms:
\[ -1.2X + 1152 = 1080 \]
\[ -1.2X = 1080 - 1152 \]
\[ -1.2X = -72 \]
\[ X = \frac{-72}{-1.2} = 60 \]

### Step 5: Find the number of male and female voters
Now substituting \( X \) back to find the number of male voters in Govindpur:
\[ \text{Male voters in Govindpur} = 7X = 7 \times 60 = 420 \]
\[ \text{Female voters in Govindpur} = 720 - 420 = 300 \]

For Vasantpur:
\[ \text{Male voters in Vasantpur} = 10X = 10 \times 60 = 600 \]
\[ \text{Female voters in Vasantpur} = 1.6(720 - 420) = 1.6 \times 300 = 480 \]

### Step 6: Find the ratio of male voters in Govindpur to female voters in Vasantpur
The ratio is:
\[ \text{Ratio} = \frac{\text{Male voters in Govindpur}}{\text{Female voters in Vasantpur}} = \frac{420}{480} \]
Simplifying this ratio:
\[ \frac{420 \div 60}{480 \div 60} = \frac{7}{8} \]

### Final Answer
The ratio of male voters in Govindpur to female voters in Vasantpur is \( \frac{7}{8} \).