A school announces that for a certain competitions, the cash price will be distributed for all the participants equally as shown below.
| Number of participants (\(x\)) | \(2\) | \(4\) | \(6\) | \(8\) | \(10\) |
| Amount for each participant in \(₹\) (\(y\)) | \(120\) | \(60\) | \(40\) | \(30\) | \(24\) |
(i) Obtain the constant of variation.
(ii) Graph the above data and hence, Compute how much will each participant get if the number of participants are \(12\).
Answer:
From the given table, as number of participants(\(x\)) , the amount for each participant(\(y\)) . This kind of proportionality is called .
(i) The constant of variation is .
(ii) Let us plot the points \((2, 120)\), \((4, 60)\), \((6, 40)\), \((8, 30)\) and \((10, 24)\) in the graph and join them to get a free-hand smooth curve.
From the graph, we can see that the relation \(xy =\) forms a .
Each participant receives \(Rs.) when there are \(12\) participants.