question_answer 1)

                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)	1,00,000	50,000	?	?	?	?	?

Answer:

                \[1\times 1,00,000=4\times x\] \[\Rightarrow \]               \[x=\frac{1,00,000}{4}=25,000\] \[1\times 1,00,000=5\times y\] \[\Rightarrow \]               \[y=\frac{1,00,000}{5}=20,000\] \[1\times 1,00,000=8\times z\] \[\Rightarrow \]               \[z=\frac{1,00,000}{8}=12,500\] \[1\times 1,00,000=10\times t\] \[\Rightarrow \]               \[t=\frac{1,00,000}{10}=10,000\] \[1\times 1,00,000=20\times w\] \[\Rightarrow \]               \[w=\frac{1,00,000}{20}=5,000\]

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

Since \[1\times 1,00,000=2\times 50,000=4\times 25,000\]\[=5\times 20,000=8\times 12,500=10\times 10,000\]\[=20\times 5,000\], so we find that the prize money given to an individual winner is inversely proportional to the number of winners.