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On a wall of dimension \[10.5\] m long and \[8.5\] m wide a square shaped wall poster is stuck at the center whose measure is \[2.5\] m. If the remaining part of the wall is to be painted with pink colour costing Rs.\[12\] per sq m the amount to be spend is

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Last updated date: 20th Jun 2024
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Answer
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Hint:To find the cost of painting the wall is by subtraction of the poster dimension by the wall dimension.
First we find the dimensional area of the wall is given as:
Area of the wall \[=\text{Length of the Wall}\times \text{Breadth of the Wall}\]
Secondly, the area of the poster is given as:
Area of the poster \[=\text{Length of Poster}\times \text{Breadth of Poster}\]
Now to find the cost of painting the wall pink is:
\[=\text{Cost per Square meter}\times \left( \left( \text{Length of the Wall}\times \text{Breadth of the Wall} \right)-\left( \text{Length of Poster}\times \text{Breadth of Poster} \right) \right)\]

Complete step by step solution:
According to the question given, the dimensions of the wall are \[10.5\] m long and \[8.5\] m wide.
Hence, using the formula to find the value of the area of the wall is given as:
Area of the wall \[=\text{Length of the Wall}\times \text{Breadth of the Wall}\]
Placing the values in the above formula, we get the value of the area of the wall as:
Area of the wall \[=10.5m\times 8.5m\]
After this we remove the area of the poster hence, the area of the poster is given as:
Area of the poster \[=\text{Length of Poster}\times \text{Breadth of Poster}\]
Placing the values in the above formula, we get the value of the area of the poster as:
Area of the poster \[=2.5\times 2.5\]
Now to find the cost of painting the wall pink with the cost of painter per square meter as Rs.\[12\] is:
\[\Rightarrow \text{Cost per Square meter}\times \left( \left( \text{Length of the Wall}\times\text{Breadth of the Wall} \right)-\left( \text{Length of Poster}\times \text{Breadth of Poster} \right)\right)\]
Placing the values in the above formula, we get the total cost as:
\[\Rightarrow \text{12}\times \left( \left( 10.5\times 8.5 \right)-\left( 2.5\times 2.5 \right) \right)\]
\[\Rightarrow 996\] Rupees
Therefore, the total cost of painting the wall devoid of the poster is \[996\] Rupees.

Note: Student may get wrong if they try to subtract the dimensions of the wall by the dimensions of the poster and then try to find the cost as the walls are not cut by the poster but a particular area has been hidden hence, we subtract the area of the poster from the wall and then multiple with the cost.