Question

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

ISC BOARD 2005

NEED STEP BY STEP EXPLANATION

Answer 1

Answer:

Step-by-step explanation:

Answer 2

• The owner of the milk store can sell 1304 l per week at ₹17 / litre

Step-by-step explanation:

Let,

• $\sf{x_{1},x_{2}}$ represent the quantity of milk
• $\sf{y_{1},y_{2}}$ represent the cost of milk per litre

Given,

• 980 l = $\sf{x_{1}}$
• 1220 l = $\sf{x_{2}}$
• ₹14 = $\sf{y_{1}}$
• ₹16 = $\sf{y_{2}}$

The linear relationship between selling price and demand is,

⟼ $\sf\dfrac{y\:-\:y_1}{y_2\:-\:y_1}\:=$ $\sf\dfrac{x\:-\:x_1}{x_2\:-\:x_1}$

⟼ $\sf\dfrac{y\:-\:14}{16\:-\:14}\:=$ $\sf\dfrac{x\:-\:980}{1220\:-\:980}$

⟼ $\sf\dfrac{y\:-\:14}{{\cancel{2}}}\:=$ $\sf\dfrac{x\:-\:980}{{\cancel{240}}}$

⟼ $\sf\dfrac{y\:-\:14}{1}\:=$$\sf\dfrac{x\:-\:980}{120}$

⟼ $\sf{120\:(y\:-\:14)\:=\:x\:-\:980}$

⟼ $\sf{120\:(y\:-\:14)\:+\:980\:=\:x}$

Substituting 'x',

$\sf{When\:y\:=\:₹17 / l,}$

⟼ $\sf{x\:=\:120\:(y\:-\:14)\:+\:980}$

⟼ $\sf{x\:=\:120\:(17\:-\:14)\:+\:980}$

⟼ $\sf{x\:=\:120\:(3)\:+\:980}$

⟼ $\sf{x\:=\:360\:+\:980}$

⟼ $\sf{x\:=\:1340}$

• Hence, the owner of the milk store can sell 1304 l per week at ₹17 / litre