Calculating Cloth Cost Using Proportions

This problem involves finding the cost of a specific length of cloth when the cost of another length is known. We can solve this using the concept of unitary method or proportions, as the cost of cloth is directly proportional to its length.

Method 1: Using the Unitary Method

The unitary method helps us find the value of a single unit first, and then use it to find the value of the required number of units.

• Step 1: Find the cost of 1 metre of cloth.

  We know that 12 metres of cloth costs ₹480.

  To find the cost of 1 metre, we divide the total cost by the total number of metres:

  Cost per metre = $ \frac{\text{Total Cost}}{\text{Total Metres}} $

  Cost per metre = $ \frac{₹480}{12 \text{ metres}} $

  Cost per metre = $ ₹40 $ per metre.

• Step 2: Calculate the cost of 18 metres of cloth.

  Now that we know the cost of 1 metre is ₹40, we can find the cost of 18 metres by multiplying the cost per metre by 18.

  Cost of 18 metres = Cost per metre $ \times $ Number of metres

  Cost of 18 metres = $ ₹40/\text{metre} \times 18 \text{ metres} $

  Cost of 18 metres = $ ₹720 $.

Method 2: Using Proportions

We can set up a direct proportion between the length of the cloth and its cost.

Let the cost of 18 metres of cloth be $ x $. The ratio of cost to length is constant.

We can write the proportion as:

$ \frac{\text{Cost}_1}{\text{Length}_1} = \frac{\text{Cost}_2}{\text{Length}_2} $

Plugging in the given values:

$ \frac{₹480}{12 \text{ metres}} = \frac{x}{18 \text{ metres}} $

To solve for $ x $, we can cross-multiply or rearrange the equation:

$ x = \frac{₹480 \times 18 \text{ metres}}{12 \text{ metres}} $

First, simplify the fraction $ \frac{18}{12} $. Both are divisible by 6:

$ \frac{18}{12} = \frac{3}{2} $

So, the equation becomes:

$ x = ₹480 \times \frac{3}{2} $

Now, divide 480 by 2:

$ \frac{480}{2} = 240 $

Finally, multiply the result by 3:

$ x = ₹240 \times 3 $

$ x = ₹720 $

Summary Table

Conclusion

Therefore, 18 metres of the same cloth will cost ₹720.