8th Class Mathematics Direct and Inverse Proportions

  • question_answer 12)                 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.

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