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.
If 65% and 60% of total male and female voters are literate in Govindpur, then find total illiterate voters in Govindpur are what percent less than total female voters in Vilaspur?

Options

A. `33.25%`
B. `31.25%`
C. `35.25%`
D. `30.25%`

Answer

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

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

Let the common multiplier be \( A \).

Thus, we can express the number of voters in each village as:
- Vasantpur = \( 27A \)
- Govindpur = \( 18A \)
- Vilashpur = \( 25A \)

Setting up the equation:
\[ 27A + 18A + 25A = 2800 \]
\[ 70A = 2800 \]
\[ A = \frac{2800}{70} = 40 \]

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

From the total voters in each village:
- Male voters in Vasantpur = \( 10X \)
- Female voters in Vasantpur = \( 1080 - 10X \)
- Male voters in Govindpur = \( 7X \)
- Female voters in Govindpur = \( 720 - 7X \)

### Step 3: Relate female voters in Vasantpur to those in Govindpur
It is given that the total female voters in Vasantpur are 60% more than those in Govindpur:
\[ 1080 - 10X = 1.6(720 - 7X) \]

Expanding and simplifying:
\[ 1080 - 10X = 1152 - 11.2X \]
\[ 1.2X = 72 \]
\[ X = 60 \]

Now substituting \( X \) back to find the number of male and female voters:
- Male voters in Vasantpur = \( 10 \times 60 = 600 \)
- Female voters in Vasantpur = \( 1080 - 600 = 480 \)
- Male voters in Govindpur = \( 7 \times 60 = 420 \)
- Female voters in Govindpur = \( 720 - 420 = 300 \)

### Step 4: Calculate male voters in Vilashpur
It is given that total male voters in Vilashpur are \( 42\frac{6}{7}\% \) more than total male voters in Govindpur. This can be expressed as:
\[ \text{Male voters in Vilashpur} = 420 + \left(\frac{300}{7} \times 420\right) \]
Calculating:
\[ \text{Male voters in Vilashpur} = 420 + \frac{300}{7} \times 420 = 420 + 180 = 600 \]
Thus, total voters in Vilashpur = 1000, so female voters in Vilashpur = \( 1000 - 600 = 400 \).

### Step 5: Calculate illiterate voters in Govindpur
Literate male voters in Govindpur = \( 65\% \) of \( 420 \):
\[ \text{Literate male} = 0.65 \times 420 = 273 \]
Illiterate male voters = \( 420 - 273 = 147 \)

Literate female voters in Govindpur = \( 60\% \) of \( 300 \):
\[ \text{Literate female} = 0.60 \times 300 = 180 \]
Illiterate female voters = \( 300 - 180 = 120 \)

Total illiterate voters in Govindpur = \( 147 + 120 = 267 \).

### Step 6: Find the percentage of illiterate voters in Govindpur compared to female voters in Vilashpur
We need to find out what percent less the total illiterate voters in Govindpur are than the total female voters in Vilashpur:
\[ \text{Difference} = 400 - 267 = 133 \]
Percentage less:
\[ \text{Percentage} = \left(\frac{133}{400}\right) \times 100 = 33.25\% \]

### Final Answer
The total illiterate voters in Govindpur are **33.25%** less than the total female voters in Vilashpur.

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