Question

The cost of the milk per litre is 15. Draw the graph for the relation between the quantity and the cost. Hence, find:
A.The proportionality constant
B.The cost of 3 litres of milk

Answer 1

Hint: We will draw the graph by the firstly calculating the values of milk per litre individually. We will then find the proportionality constant K by the formula:
K= (cost of milk at A – cost of milk at B) / (amount of milk at A – amount of milk at B) from the graph.
Then, we will check from the graph what is the cost of 3 litres of milk.

Complete step-by-step answer:
We are given the cost of milk per litre as Rs. 15
Then, we can say that the cost of 2 litres of milk will be 2 $ \times $15 = Rs. 30
Similarly, for 3 litres of milk, the cost will be Rs. 45
Let us say that Y denotes the cost of the milk and X denotes the amount of milk. Then, we can write the above condition as:
X: 1 2 3 4 5 6 7 8 …
Y: 15 30 45 60 75 90 105 120 …
Plotting these values on a graph, we get

Now, for the proportionality constant K, let us assume any points A and B on the graph.
The proportionality constant is defined as:
K= (cost of milk at A – cost of milk at B) / (amount of milk at A – amount of milk at B)
Therefore, the cost of milk at A = 90 and at B = 60.
The amount of milk (in litres) at A = 6 and at B = 4.
Applying these values in the formula, we get
$K = \dfrac{{\left( {90 - 60} \right)}}{{\left( {6 - 4} \right)}} = \dfrac{{30}}{2} = 15$
Hence, the proportionality constant is 15.
By observation from the graph, we can say that the cost of 3 litres of milk is Rs. 45.

Note: In such questions, you may get confused about the values which need to be plotted on the graph since we need to calculate them by ourselves based on the prior information given in the question.