State whether the following statement is true or false.

The prize money of ₹ 1,00,000 is to be divided equally amongst the winners in a video game competition.

The prize money given to an individual winner is inversely proportional to the number of winners.

Question

State whether the following statement is true or false.

The prize money of ₹ 1,00,000 is to be divided equally amongst the winners in a video game competition.

The prize money given to an individual winner is inversely proportional to the number of winners.

Accepted Answer

The given table shows the prize money of ₹ 1,00,000 is divided equally amongst the winners in a video game competition.We know from the concept of proportionality that; two numbers are said to vary inversely if their product is constant for every particular value. Let

x
    and

y
   be that two numbers, then

xy=k
  , where

k
  =constant.From the available data in the table, it is observed that if the winner's number increases, then prize money decreases. From the two data, we have,

1×100000=2×50000=100000
  So, (Number of winners)× (Prize of each winner) = k = 100000.When number of winners is 4, the prize money of each winner will be,

⇒
      
       100000
      4

⇒25000

When number of winners is 5, the prize money of each winner will be,

⇒
      
       100000
      5

⇒20000

When number of winners is 8, the prize money of each winner will be,

⇒
      
       100000
      8

⇒12500

When number of winners is 10, the prize money of each winner will be,

⇒
      
       100000
      
       10

⇒10000

When number of winners is 20, the prize money of each winner will be,

⇒
      
       100000
      
       20

⇒5000

Therefore, the complete table is given below.Number of winners124581020Prize money of each winner (₹)10000050000250002000012500100005000It is observed that if the winner's number increases, then prize money decreases.So, the prize money given to an individual winner is inversely proportional to the number of winners.Thus, the given statement is true.Hence, option 1 is correct.