If the cost of 120 m of cloth is Rs. 9,600, then what will be the cost of 147 m of that cloth?
Calculating Cloth Cost Using Direct Proportion
This problem involves calculating the cost of a specific length of cloth given the cost of a different length. This type of problem can be solved using the concept of direct proportion.
In this case, the cost of the cloth is directly proportional to its length. This means that if the length of the cloth increases, the cost also increases proportionally, and if the length decreases, the cost decreases proportionally.
Steps to Solve the Cloth Cost Problem
To find the cost of 147 m of cloth, we can first find the cost of 1 meter of the cloth. Once we know the cost per meter, we can easily calculate the cost for any other length.
- Find the cost of 1 meter of cloth.
- Multiply the cost per meter by the required length (147 m).
Calculating Cost Per Meter
We are given that the cost of 120 m of cloth is Rs. 9,600.
Cost of 1 meter of cloth = $\frac{\text{Total Cost}}{\text{Total Length}}$
Cost of 1 meter of cloth = $\frac{Rs.\ 9600}{120\ m}$
Let's perform the division:
Cost of 1 meter of cloth = $Rs.\ \frac{960}{12}$
Cost of 1 meter of cloth = $Rs.\ 80$ per meter.
So, the cost of 1 meter of that cloth is Rs. 80.
Calculating the Cost of 147 m of Cloth
Now that we know the cost of 1 meter, we can find the cost of 147 meters.
Cost of 147 m of cloth = Cost per meter $\times$ Length
Cost of 147 m of cloth = $Rs.\ 80 \times 147$
Let's multiply 80 by 147:
$ \begin{array}{@{}c@{\,}c} & 147 \\ \times & 80 \\ \hline & 000 \\ + & 11760 \\ \hline & 11760 \\ \end{array} $
Cost of 147 m of cloth = Rs. 11,760.
Therefore, the cost of 147 m of that cloth will be Rs. 11,760.
Verifying the Cloth Cost Calculation
The calculated cost of Rs. 11,760 for 147 m of cloth is higher than the cost of Rs. 9,600 for 120 m, which makes sense because 147 m is a greater length than 120 m, and the cost should increase with length in a direct proportion scenario.
| Length of Cloth (m) | Cost (Rs.) |
|---|---|
| 120 | 9600 |
| 1 | 80 (9600 / 120) |
| 147 | 11760 (80 * 147) |
Revision Table: Key Concepts
| Concept | Description | Application in this Problem |
|---|---|---|
| Direct Proportion | Two quantities are in direct proportion if an increase in one quantity causes a proportional increase in the other, and vice versa. Their ratio is constant. | Cost of cloth is directly proportional to its length. $\frac{\text{Cost}}{\text{Length}} = \text{Constant}$ |
| Unit Method | Finding the value of a single unit of a quantity to calculate the value of any required number of units. | First, find the cost of 1 meter of cloth (the unit cost). Then, use the unit cost to find the cost of 147 meters. |
Additional Information on Direct Proportion and Unit Method
Direct proportion is a fundamental concept in mathematics used to solve various real-world problems involving quantities that change together at a constant rate. Examples include distance covered and time taken at a constant speed, amount of work done and number of workers (sometimes, but be careful with inverse proportion here), or amount of ingredients and number of servings in a recipe.
The unit method is a straightforward way to solve problems involving direct proportion. It breaks down the problem into two simple steps:
- Calculate the value for a single unit. This is done by dividing the total value by the total number of units.
- Calculate the value for the required number of units. This is done by multiplying the value of a single unit by the required number of units.
This method simplifies complex proportion problems into easily manageable calculations.
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