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Question:

In a Television game show, the prize money of Rs1,00,000 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?

Solution:

Let x be the number of winners and y be the prize money for each winner. So here the total amount for prize money is the same i.e., k = x × y = 1,00,000
Let x1 be the prize for 4 people, ⇒ 4 × x1 = 100000 ⇒ x1 = 25000
Similarly,
For 5 people, x2 = 20000
For 8 people, x3 = 12500
For 10 people, x4 = 10000
For 20 people, x5 = 5000
As the number of winners increases, the prize money for each winner decreases. Therefore, the prize money given to an individual winner is inversely proportional to the number of winners.