Question

17. 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?




11th cbse maths chapter 10​

Answer 1

Answer:

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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