Question

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

Answer 1

$\text{Let price and litre be denoted in ordered pair (x, y) where x denotes the Rs per litre and y denotes the quantity of milk in litre.}\text{Given, (14, 980) and (16, 1220) are two points.}\text{Let linear relations i.e., linear equation is}y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\Rightarrow y-980=\frac{1220-980}{16-14}(x-14)\Rightarrow y-980=\frac{240}{2}(x-14)(\because x_1=14,y_1=980,x_2=16,y_2=1220)\Rightarrow y-980=120(x-14)\Rightarrow y-980=120x-120\times 14\Rightarrow 120x-y=1680-980\Rightarrow 120x-y=700\text{When price x = 17}\Rightarrow 120\times 17-y=700\Rightarrow y=2040-700y=1340\text{He will sell weekly 1340 L milk at the rate of Rs 17 L.}$