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?
 

Number of winners	1	2	4	5	8	10	20
Prize for each winner (in Rs)	100000	50000	…	…	…	…	…

Answer 1

A table of the given information is as follows.
 

Number of winners	1	2	4	5	8	10	20
Prize for each winner (in Rs)	100000	50000	x1	x2	x3	x4	x5

From the table, we obtain 1 × 100000 
\(= 2 × 50000 \)
= 100000
Thus, the number of winners and the amount given to each winner are inversely proportional to each other. 
Therefore, 
\(1 × 100000 = 4 × x_1\)
\(x_1 = \frac{1 × 100000}{4}\)
\(x_1 = 25000\)

\(1 × 100000 = 5 × x_2\)
\(x_2 = \frac{1 × 100000}{5}\)
\(x_2 = 20000\)

\(1 × 100000 = 8 × x_3\)
\(x_3 =\frac{ 1 × 100000}{8}\)
\(x_3 = 12,500\)

\(1 × 100000 = 10 × x_4\)
\(x_4 = \frac{1 × 100000}{10}\)
\(x_4 = 10000\)

\(1 × 100000 = 20 × x_5\)
\(x_5 = \frac{1 × 100000}{20}\)
\(x_5 = 5000\)