An order was placed for the supply of a carpet whose breadth was 6 m and whose length was 1.44 times the breadth. What is the cost of a carpet whose length and breadth are 40% more and 25% more, respectively, than the first carpet? [The cost of a carpet is ₹45/m2]
₹4082.40
Carpet Dimensions Calculation
The problem asks us to find the cost of a new carpet based on the dimensions of an initial carpet and given percentage increases. Let's break this down step-by-step.
First, we determine the dimensions of the first carpet.
- The breadth of the first carpet is given as \( B_1 = 6 \) m.
- The length of the first carpet is 1.44 times its breadth. So, \( L_1 = 1.44 \times B_1 \).
- Calculating the length \( L_1 \): \( L_1 = 1.44 \times 6 \) m = \( 8.64 \) m.
New Carpet Dimensions Calculation
Next, we need to find the dimensions of the second carpet, which are described as percentage increases from the first carpet's dimensions.
- The length of the second carpet (\( L_2 \)) is 40% more than the first carpet's length (\( L_1 \)).
- This means \( L_2 = L_1 + (40\% \text{ of } L_1) \).
- Using the formula for percentage increase: \( L_2 = L_1 \times (1 + \frac{40}{100}) = L_1 \times (1 + 0.40) = 1.40 \times L_1 \).
- Calculating the new length \( L_2 \): \( L_2 = 1.40 \times 8.64 \) m = \( 12.096 \) m.
- The breadth of the second carpet (\( B_2 \)) is 25% more than the first carpet's breadth (\( B_1 \)).
- Using the formula for percentage increase: \( B_2 = B_1 \times (1 + \frac{25}{100}) = B_1 \times (1 + 0.25) = 1.25 \times B_1 \).
- Calculating the new breadth \( B_2 \): \( B_2 = 1.25 \times 6 \) m = \( 7.5 \) m.
New Carpet Area Calculation
With the dimensions of the second carpet calculated, we can now find its area (\( A_2 \)).
- The area of a rectangle is length multiplied by breadth: \( A_2 = L_2 \times B_2 \).
- Calculating the area \( A_2 \): \( A_2 = 12.096 \) m \(\times\) \( 7.5 \) m = \( 90.72 \) m\(^2\).
Total Cost Calculation
Finally, we calculate the cost of the new carpet using its area and the given cost rate.
- The cost rate is given as \( ₹45 \) per square meter (₹45/m\(^2\)).
- The total cost is the area of the carpet multiplied by the cost rate.
- Total Cost = \( A_2 \times ₹45/\text{m}^2 \).
- Calculating the total cost: Total Cost = \( 90.72 \times 45 \).
- Total Cost = \( ₹4082.40 \).
Therefore, the cost of the new carpet is ₹4082.40.
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