Question 27 of 70intermediate🔧 ApplyShort Answer4 marks

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?

Correct Answer

1340 litres

Exercise: EXERCISE 9.2 | Q: 16 | (Chapter: 14)
For More Understanding

Explanation

This problem involves finding a linear relationship between price and demand. We treat price as the independent variable (x) and demand as the dependent variable (y). Using the two given data points, we can find the equation of the line and then calculate the demand at the new price.

Solution Steps

  1. Step 1: Let selling price (in Rs) = x and demand (in litres) = y. We have two points: (14, 980) and (16, 1220).

  2. Step 2: Find the slope m of the line: m = (1220 - 980)/(16 - 14) = 240/2 = 120.

  3. Step 3: Using point-slope form, y - y₁ = m(x - x₁), we get: y - 980 = 120(x - 14).

  4. Step 4: Simplify to get the linear equation: y - 980 = 120x - 1680, therefore y = 120x - 700.

  5. Step 5: Find demand at Rs 17/litre: y = 120(17) - 700 = 2040 - 700 = 1340 litres.

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