`4/5` th of the voters in Delhi promised to vote for Sonu and the rest promised to vote for Monu. Of these voters, 10% of the voters who had promised to vote for Sonu, did not vote on the election day, while 20% of the voters who had promised to vote for Monu did not vote on the election day. What is the total no. of votes polled if Sonu got 216 votes ?

Options

A. 300
B. 100
C. 290
D. 264

Answer

To solve the problem step by step, we will follow the reasoning provided in the video transcript.

### Step 1: Define the total number of voters
Let the total number of voters in Delhi be represented by \( x \).

### Step 2: Calculate the number of voters who promised to vote for Sonu and Monu
According to the question, \( \frac{4}{5} \) of the voters promised to vote for Sonu. Therefore, the number of voters who promised to vote for Sonu is:
\[ \text{Voters for Sonu} = \frac{4}{5} x \]
The remaining voters promised to vote for Monu, which is:
\[ \text{Voters for Monu} = x - \frac{4}{5} x = \frac{1}{5} x \]

### Step 3: Calculate the number of voters who actually voted for Sonu
It is given that 10% of the voters who promised to vote for Sonu did not vote. Therefore, 90% of them did vote. The number of voters who actually voted for Sonu is:
\[ \text{Votes for Sonu} = 90\% \text{ of } \left(\frac{4}{5} x\right) = \frac{9}{10} \times \frac{4}{5} x = \frac{36}{50} x = \frac{18}{25} x \]

### Step 4: Set up the equation based on the votes received by Sonu
We know from the problem that Sonu received 216 votes. Therefore, we can set up the equation:
\[ \frac{18}{25} x = 216 \]

### Step 5: Solve for \( x \)
To find \( x \), we can rearrange the equation:
\[ x = 216 \times \frac{25}{18} \]
Calculating this gives:
\[ x = 216 \div 18 \times 25 = 12 \times 25 = 300 \]

### Step 6: Conclusion
The total number of voters in Delhi is \( x = 300 \).

### Step 7: Verify the calculations for Monu
Now, let's find the number of voters who promised to vote for Monu:
\[ \text{Voters for Monu} = \frac{1}{5} x = \frac{1}{5} \times 300 = 60 \]
20% of these voters did not vote, so 80% did vote:
\[ \text{Votes for Monu} = 80\% \text{ of } 60 = 0.8 \times 60 = 48 \]

### Step 8: Total votes polled
The total votes polled would then be:
\[ \text{Total votes} = \text{Votes for Sonu} + \text{Votes for Monu} = 216 + 48 = 264 \]

Thus, the total number of votes polled is 264.

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