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

Options

A. `1340`
B. `1530`
C. `1220`
D. `1635`

Explanation

To solve the problem, we will use the concept of linear relationships between price and demand. We have two points based on the given data:

1. At Rs 14/litre, the demand is 980 litres.
2. At Rs 16/litre, the demand is 1220 litres.

We can represent these points as coordinates:
- Point A (14, 980)
- Point B (16, 1220)

We need to find out how many litres can be sold at Rs 17/litre, which we will denote as point C (17, y).

### Step 1: Set up the linear equation

Using the two points, we can find the slope (m) of the line that represents the relationship between price (x) and demand (y). The formula for the slope between two points (x1, y1) and (x2, y2) is:

\[ m = \frac{y2 - y1}{x2 - x1} \]

Substituting the values:

\[ m = \frac{1220 - 980}{16 - 14} = \frac{240}{2} = 120 \]

### Step 2: Use the point-slope form of the equation of a line

Now that we have the slope, we can use the point-slope form of the equation of a line, which is:

\[ y - y1 = m(x - x1) \]

We can use point A (14, 980) for this:

\[ y - 980 = 120(x - 14) \]

### Step 3: Simplify the equation

Now we will simplify the equation:

\[ y - 980 = 120x - 1680 \]

Adding 980 to both sides gives:

\[ y = 120x - 1680 + 980 \]

\[ y = 120x - 700 \]

### Step 4: Find the demand at Rs 17/litre

Now we substitute x = 17 into the equation to find y:

\[ y = 120(17) - 700 \]

Calculating this:

\[ y = 2040 - 700 = 1340 \]

### Conclusion

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

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