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?

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Solution

$\begin{matrix} N u m b e r o f w i n n e r s & 1 & 2 & 4 & 5 & 8 & 10 & 20 P r i z e f o r e a c h w i n n e r (I n R u p e e s) & 100000 & 50000 & y 3 & y 4 & y 5 & y 6 & y 7 \end{matrix}$

Hence the constant k = xy = 1,00,000

"x" is Number of winners and "y" is prize for each winner.
Hence, x3y3 = 1,00,000
⇒ 4×y3 = 100000
⇒ y3 = $\frac{100000}{4}$ = 25000
Similarly,
y4 = $\frac{100000}{5}$ = 20000
y5 = $\frac{100000}{8}$ = 12500
y6 = $\frac{100000}{10}$ = 10000
y7 = $\frac{100000}{20}$ = 5000

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