Question : The internal length of a room is two times its breadth and three times its height. The total cost of painting its four walls at the rate of INR 25/m2 is INR 3,600. What is the cost of laying a carpet on its floor at the rate of INR 90.50/m2?
Option 1: INR 6,516
Option 2: INR 7,240
Option 3: INR 5,430
Option 4: INR 5,970
Correct Answer: INR 6,516
Solution : The total cost of painting its four walls at the rate of INR 25/m$^2$ is INR 3,600. Rate = INR 90.50 per m$^2$ The area of four walls, A = $2(l + b)h$, where $l,b$ and $h$ are the length, breadth and height respectively. Area of floor = $l × b$ Let the length of the room be $6x$. Breadth of the room $=\frac{6x}{2}= 3x$ Height of the room $=\frac{6x}{3}= 2x$ Cost of painting INR 25/m$^2$ Area of four wall = $(\frac{1}{25}) × 3600$ = 144 m$^2$ So, $2(6x + 3x) × 2x = 144$ ⇒ $2x × 18x = 144$ ⇒ $36x^2 = 144$ ⇒ $x^2 = \frac{144}{36} = 4$ ⇒ $x = \sqrt{4} = 2$ Area of floor $=l × b = 6x × 3x = 6 × 2 × 3 × 2 = 72$ m$^2$ Cost of laying carpet on 1 m$^2$ = 90.50 Cost of laying carpet on = 72 m$^2$ = 90.50 × 72 = INR 6,516 Hence, the correct answer is INR 6,516.
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