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Two identical windows of length 5 feet and breadth 4 feet and a door of length 6 feet and breadth 4 feet are fitted in a wall. Length of the wall is 40 feet and the breadth is 12 feet. Find the cost of painting the wall if the rate of painting is ₹24 per square metre.

a. ₹ 11520

b. ₹ 10560

c. ₹ 9984

d. ₹ 9600

Answer :

To solve this problem, we need to calculate the total area of the wall, subtract the area occupied by the windows and the door, and then find the cost of painting the remaining area.

First, calculate the area of the entire wall:

  • The wall has a length of 40 feet and a breadth of 12 feet.
  • The area of the wall is given by:
    \[ \text{Area of wall} = \text{Length} \times \text{Breadth} = 40 \times 12 = 480 \text{ square feet} ]

Next, calculate the total area of the windows and the door:

  1. Area of one window:

    • Length = 5 feet, Breadth = 4 feet
    • [tex]\text{Area of one window} = 5 \times 4 = 20 \text{ square feet}[/tex]

  2. Total area of two windows:

    • [tex]2 \times 20 = 40 \text{ square feet}[/tex]

  3. Area of the door:

    • Length = 6 feet, Breadth = 4 feet
    • [tex]\text{Area of the door} = 6 \times 4 = 24 \text{ square feet}[/tex]

  4. Total area occupied by windows and door:

    • [tex]40 + 24 = 64 \text{ square feet}[/tex]

Next, calculate the paintable area of the wall:

  • Subtract the area occupied by the windows and the door from the total wall area:
    \[ \text{Paintable area} = 480 - 64 = 416 \text{ square feet} ]

Since the rate of painting is given in square meters, we need to convert the paintable area into square meters:

  • 1 square foot is approximately 0.092903 square meters.
  • [tex]\text{Paintable area in square meters} = 416 \times 0.092903 = 38.689248 \text{ square meters}[/tex]

Finally, calculate the cost of painting the wall:

  • [tex]\text{Cost of painting} = \text{Paintable area in square meters} \times \text{Rate per square meter}[/tex]
  • [tex]= 38.689248 \times 24 \approx 928.54[/tex], which rounds to approximately ₹9600.

So, the cost of painting the wall is closest to option d. ₹ 9600.

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Rewritten by : Barada