Shreya estimated the cost of painting the four walls of her old room to be Rs. 600. If the length, breadth and height of her new room are double of that her old room. What will be the cost of painting all the four walls of her new room?
Solution
Correct Answer: Option C
Let the length, breadth and height of old room be l. b and h respectively.
Painting is done on a surface area so cost of painting will be proportional to the surface area of the room, excluding the base area and top area.
Area to be painted = 2 × (bh + lh)
∵ Cost of Painting the above area = Rs. 600
Now, in the new room, the length, breadth and height are twice of those in the old room.
∴ New length = 2l; New breadth = 2b and new height= 2h
∴ New area to be painted = 2 × [(2b × 2h) + (2l × 2h)]
⇒ New area to be painted = 8 × (bh + lh)
∴ New cost of painting \(= \frac{{Old\;cost\;of\;painting}}{{Old\;Area}} \times New\;Area\)
⇒ New cost of painting \(= \frac{{600}}{{2\left( {bh + lh} \right)}} \times 8\left( {bh + lh} \right)\)
⇒ New cost of painting = 4 × 600 = Rs. 2400
Practice More Questions on Our App!
Download our app for free and access thousands of MCQ questions with detailed solutions