Question

"Question 2 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 … … … … …

Class 8 Direct and Inverse Proportions Page 213"

Answer 1

Direct variation:

If two quantities increase or decrease together in such a manner that the ratio of their corresponding values remain constant, we say  that the two quantities vary  directly.

In other words x and y are said to vary directly if X/y = k , where k is a positive constant.

In direct Proportion
x/y= k

x=ky

So we can find value of k from known values, and then use the formula to calculate the unknown values

 

Inverse variation:

Two quantities x and y are said to vary inversely or indirectly if an increase in x  causes a decrease in y and a decrease in X causes an increase in y in such a way that xy remains constant.

In other words x and y are said to vary indirectly if x y = k, where K is a positive constant.

In inverse Proportion
xy= k

x=k/y

So we can find value of k from known values, and then use the formula to calculate the unknown values

 

When two quantities x and y are in direct proportion (or vary directly) they are also written as x∝y.
When two quantities x and y are in inverse proportion (or vary inversely) they are also written as x∝ 1/y

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Solution is in the attachment

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Hope this will help you....

Answer 2

Number of winners 1 2 4 5 8 10 20

Prize of each winner (in Rs) 1,00,000 50,000 ⋯ ⋯ ⋯ ⋯ ⋯