In a village-X, a total of 6000 registered voters (male+female) had cast their votes in which `70%` of total registered male voters and `45%` of toal registerd female voters had voted. If total registered male voters are 2000 more than total registered female voters, then find the total number of registered voters in village-X.

Options

A. 20000
B. 15000
C. 10000
D. 5000

Answer

To solve the problem step by step, we will define the variables and set up equations based on the information provided.

### Step 1: Define Variables
Let:
- \( M \) = Total registered male voters
- \( F \) = Total registered female voters

### Step 2: Set Up the Relationship Between Male and Female Voters
According to the problem, the total registered male voters are 2000 more than the total registered female voters. This can be expressed as:
\[ M = F + 2000 \] (Equation 1)

### Step 3: Set Up the Voting Equation
We know that a total of 6000 registered voters have cast their votes. The voting percentages are given as:
- 70% of male voters voted: \( 0.7M \)
- 45% of female voters voted: \( 0.45F \)

The equation for the total votes cast can be expressed as:
\[ 0.7M + 0.45F = 6000 \] (Equation 2)

### Step 4: Substitute Equation 1 into Equation 2
Now, we will substitute \( M \) from Equation 1 into Equation 2:
\[ 0.7(F + 2000) + 0.45F = 6000 \]

### Step 5: Simplify the Equation
Expanding the equation:
\[ 0.7F + 1400 + 0.45F = 6000 \]
Combine like terms:
\[ (0.7F + 0.45F) + 1400 = 6000 \]
\[ 1.15F + 1400 = 6000 \]

### Step 6: Isolate \( F \)
Subtract 1400 from both sides:
\[ 1.15F = 6000 - 1400 \]
\[ 1.15F = 4600 \]

### Step 7: Solve for \( F \)
Now, divide both sides by 1.15 to find \( F \):
\[ F = \frac{4600}{1.15} \]
\[ F = 4000 \]

### Step 8: Find \( M \)
Using Equation 1 to find \( M \):
\[ M = F + 2000 \]
\[ M = 4000 + 2000 \]
\[ M = 6000 \]

### Step 9: Calculate Total Registered Voters
The total number of registered voters \( T \) is the sum of male and female voters:
\[ T = M + F \]
\[ T = 6000 + 4000 \]
\[ T = 10000 \]

### Final Answer
The total number of registered voters in village-X is **10,000**.

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