In an election only two candidates Ram and Shyam contested, Ram got `75%` of the total valid votes. `6%` of the polled votes were declared invalid. If 64200 votes were polled, then find the number of valid votes polled in favour of Shyam.

Answer

To find the number of valid votes polled in favor of Shyam, we can follow these steps:

### Step 1: Calculate the number of invalid votes
Given that 6% of the total votes were declared invalid, we first need to find out how many votes that is.

\[ \text{Total votes polled} = 64200 \]
\[ \text{Invalid votes} = 6\% \text{ of } 64200 = \frac{6}{100} \times 64200 = 0.06 \times 64200 = 3852 \]

### Step 2: Calculate the number of valid votes
To find the number of valid votes, we subtract the number of invalid votes from the total votes.

\[ \text{Valid votes} = \text{Total votes} - \text{Invalid votes} = 64200 - 3852 = 60348 \]

### Step 3: Calculate the number of votes received by Ram
Ram received 75% of the total valid votes. We can find out how many votes that is.

\[ \text{Votes for Ram} = 75\% \text{ of } 60348 = \frac{75}{100} \times 60348 = 0.75 \times 60348 = 45261 \]

### Step 4: Calculate the number of votes received by Shyam
Since there are only two candidates, the remaining votes will be for Shyam. Thus, we can find the number of votes for Shyam by subtracting the votes for Ram from the valid votes.

\[ \text{Votes for Shyam} = \text{Valid votes} - \text{Votes for Ram} = 60348 - 45261 = 15087 \]

### Final Answer
The number of valid votes polled in favor of Shyam is **15087**.

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