Question

In a Television game show, the prize money of $ Rs. 1,00,000$ is to be divided equally amongst the winners. Complete the following table and find whether the prize money given to an individual winner is directly or inversely proportional to the number of winners:

\begin{tabular}{|l|l|l|l|l|l|l|l|} \hline No. of winners & 1 & 2 & 4 & 5 & 8 & 10 & 20 \\ \hline Prize for each winner (in Js \( _{ Rs } \) & \( 1,00,000 \) & 50,000 & \( \cdots \) & \( \cdots \) & \( \cdots \) & \( \cdots \) & \( \ldots \) \\ \hline \end{tabular}

Answer 1

Step 1 Compute the prize money per winner.

Now, find the prize money per winner when there are $4$ winners.

$\frac{1,00,000}{4}=25,000$

So, the prize money per winner will be $Rs.25,000$ when there are $4$ winners.

$\Rightarrow$The prize money per winner when there are $5$ winners.

$\frac{1,00,000}{5}=20,000$

So, the prize money per winner will be $Rs.20,000$ when there are $5$ winners.

$\Rightarrow$The prize money per winner when there are $5$ winners.

$\frac{1,00,000}{5}=20,000$

So, the prize money per winner will be $Rs.20,000$ when there are $5$ winners.

$\Rightarrow$The prize money per winner when there are $8$ winners.

$\frac{1,00,000}{8}=12,500$

So, the prize money per winner will be $Rs.12,500$ when there are $8$ winners.

$\Rightarrow$The prize money per winner when there are $10$ winners.

$\frac{1,00,000}{10}=10,000$

So, the prize money per winner will be $Rs.10,000$ when there are $10$ winners.

$\Rightarrow$The prize money per winner when there are $20$ winners.

$\frac{1,00,000}{20}=5,000$

So, the prize money per winner will be $Rs.5,000$ when there are $20$ winners.

Step 2 Complete the table.

Insert all the calculated values in the given table as follows:

$\text{Number of winners}$	$1$	$2$	$4$	$5$	$8$	$10$	$20$
$\text{Prize for each winner (in Rs.)}$	$1,00,000$	$50,000$	$25,000$	$20,000$	$12,500$	$10,000$	$5,000$

Since, As the number of winners increases the prize money per winner decreases.

Therefore, the prize money given to an individual winner is inversely proportional to the number of winners.