# The owner of a milk store finds that, he can sell 980 litres of milk each week at Rs 14/litre and 1220 litres of milk each week at Rs 16/litre.

Question:

The owner of a milk store finds that, he can sell 980 litres of milk each week at Rs 14/litre and 1220 litres of milk each week at Rs 16/litre. Assuming a linear relationship between selling price and demand, how many litres could he sell weekly at Rs 17/litre?

Solution:

The relationship between selling price and demand is linear.

Assuming selling price per litre along the x-axis and demand along the y-axis, we have two points i.e., (14, 980) and (16, 1220) in the XY plane that satisfy the linear relationship between selling price and demand.

Therefore, the linear relationship between selling price per litre and demand is the equation of the line passing through points (14, 980) and (16, 1220).

$y-980=\frac{1220-980}{16-14}(x-14)$

$y-980=\frac{240}{2}(x-14)$

$y-980=120(x-14)$

i.e., $y=120(x-14)+980$

When x = Rs 17/litre,

$y=120(17-14)+980$

$\Rightarrow y=120 \times 3+980=360+980=1340$

Thus, the owner of the milk store could sell 1340 litres of milk weekly at Rs $17 /$ litre.