Q2. In a Television game show, the prize money of ` 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?

Number of winners

    1     2  4  5   8  10  20

Prize for each winner (in Rs.)

 1,00,000  50,000 .... .... .... .... ....

 

 

 

Answers (1)

Let us assume that for the number of winners 4, 5, 8, 10 and 20 are x1, x2, x3, x4, and x5 respectively and given that the prize money of Rs. 1,00,000 is to be divided equally amongst the winners.

Thus we have,

For 4 number of winners:

\frac{Rs.1,00,000}{4}=Rs.25,000

So Rs. 25,000 to be distributed among each.

For 5 number of winners:

\frac{Rs.1,00,000}{5}=Rs.20,000 

So Rs. 20,000to be distributed among each.

For 8 number of winners:

\frac{Rs.1,00,000}{8}=Rs.12,500 

So Rs. 12,500 to be distributed among each.

For 10 number of winners:

\frac{Rs.1,00,000}{10}=Rs.10,000

 So Rs. 10,000 each would get.

similarly for 20 number of winners:

\frac{Rs.1,00,000}{20}=Rs.5,000 

So Rs. 5000 each would get.

Hence we have;

Number of winners (x) 1 2 4 5 8 10 20
Prize for each winner (in ? ) (y) 1,00,000 50,000 25,000 20,000 12,500 10,000 5,000

 

Two quantities x and y are said to be in inverse proportional if they satisfy the given relation;

xy=k; where k is a constant.

Calculating xy: 

xy=1\times1,00,000=2\times50,000=4\times25,000=5\times20,000=8\times12,500=10\times10,000=20\times5,000=1,00,000

Clearly, we can see that the prize money given to an individual winner is inversely proportional.

 

 

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