In a village, `40%` of the registered voters are female. `80%` of male registered voters, and `60%` of female registered voters cast their votes in the election. If only two candidates were contesting the election and respective ratio of number of votes received by them is `5:4`, what per cent of registered voters (male aid female) cast their votes for the winning candidate?

Options

A. 55
B. 50
C. 35
D. 40

Answer

To solve the problem step by step, we will break it down as follows:

### Step 1: Determine the number of registered voters
Assume the total number of registered voters in the village is 100.

### Step 2: Calculate the number of female and male voters
- Female voters = 40% of 100 = 40
- Male voters = 100 - 40 = 60

### Step 3: Calculate the number of voters who cast their votes
- Female voters who cast their votes = 60% of 40 = (60/100) * 40 = 24
- Male voters who cast their votes = 80% of 60 = (80/100) * 60 = 48

### Step 4: Calculate the total number of votes cast
Total votes cast = Female votes + Male votes = 24 + 48 = 72

### Step 5: Determine the ratio of votes received by the candidates
The ratio of votes received by the two candidates is 5:4. Let the votes received by the winning candidate be 5x and the votes received by the losing candidate be 4x.

### Step 6: Set up the equation based on total votes
According to the ratio:
5x + 4x = Total votes cast
9x = 72
x = 72 / 9 = 8

### Step 7: Calculate the votes received by the winning candidate
Votes for the winning candidate = 5x = 5 * 8 = 40

### Step 8: Calculate the percentage of registered voters who voted for the winning candidate
Percentage of registered voters who voted for the winning candidate = (Votes for winning candidate / Total registered voters) * 100
= (40 / 100) * 100 = 40%

### Final Answer
Thus, the percentage of registered voters (male and female) who cast their votes for the winning candidate is **40%**.

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