Answer:
Rs 4650 or 465000 paisa
Step-by-step explanation:
Question:
A saree 4.5 m long and 1.2 m wide has a 25 cm wide border all around it on the inside. Find the cost of weaving the border at 15 paise per cm².
Answer:
To find the cost of weaving the border, let's start by converting the dimensions from meters to centimeters since the cost is given in paise per square centimeter.
Given:
- Length of the saree = 4.5 m
- Width of the saree = 1.2 m
- Width of the border = 25 cm
We need to convert the length and width of the saree from meters to centimeters:
1 meter = 100 centimeters.
So, the length of the saree in centimeters = [tex]4.5 \times 100 = 450[/tex] cm, and the width of the saree in centimeters = [tex]1.2 \times 100 = 120[/tex] cm.
Now, let's calculate the new dimensions of the saree including the border:
- Length of the saree with border = [tex]450 + 2 \times 25[/tex] cm
- Width of the saree with border = [tex]120 + 2 \times 25[/tex] cm
Then, we can calculate the area of the saree with the border and the area of just the border.
Area of the saree with the border:
[tex] \textsf{Area} = \textsf{Length} \times \textsf{Width} [/tex]
Area of just the border:
[tex] \textsf{Border Area} = (\textsf{Length with border} \times \textsf{Width with border}) - (\textsf{Length} \times \textsf{Width}) [/tex]
Finally, we multiply the area of the border by the cost per square centimeter to find the total cost of weaving the border.
Let's compute:
Length of the saree with border
= [tex]450 + 2 \times 25 = 500[/tex] cm
Width of the saree with border
= [tex]120 + 2 \times 25 = 170[/tex] cm
Area of the saree with the border:
[tex] \textsf{Area} = 500 \times 170 \textsf{ cm}^2 [/tex]
Area of just the border:
[tex] \textsf{Border Area} = (500 \times 170) - (450 \times 120) \textsf{ cm}^2 [/tex]
Finally, the cost of weaving the border:
[tex] \textsf{Cost} = \textsf{Border Area} \times 15 \textsf{ paise per cm}^2 [/tex]
Let's do the calculations:
[tex] \textsf{Area} = 500 \times 170 = 85000 \textsf{ cm}^2 [/tex]
[tex] \textsf{Border Area} = (500 \times 170) - (450 \times 120) \textsf{ cm}^2 [/tex]
[tex] = 85000 - 54000 = 31000 \textsf{ cm}^2 [/tex]
[tex] \textsf{Cost} = 31000 \times 15 \textsf{ paise} [/tex]
[tex] = 465000 \textsf{ paise} [/tex]
Since 100 paise make 1 rupee, the cost in rupees is:
[tex] \textsf{Cost} = \dfrac{465000}{100} \textsf{ rupees} = 4650 \textsf{ rupees} [/tex]
So, the cost of weaving the border is 4650 rupees.
