A room is half as long again as it is broad. The cost of carpeting the room at Tk. 5 per sq. m is Tk. 270 and the cost of papering the four walls at Tk. 10 per m$^{2}$ is Tk. 1,720. If a door and 2 windows occupy 8 sq. m. find the dimensions of the room.

Ashifur August 8, 2023 - 18:56

Problem: A room is half as long again as it is broad. The cost of carpeting the room at Tk. 5 per sq. m is Tk. 270 and the cost of papering the four walls at Tk. 10 per m$^{2}$ is Tk. 1,720. If a door and 2 windows occupy 8 sq. m. find the dimensions of the room.

View all: PUBALI BANK OFFICER (SO|OFFICER) | WRITTEN QUESTION (MATH) SOLVE | 2016

Correct Answer: The dimensions of the room is Length= 9m, Breadth= 6m, height= 6m

Explanation:

Let the dimension of the room Breadth =x meter, Length = x+ $\frac{x}{2}$ meter and Height = h meterThe carpet area = Area of the floor = Length x Breadth = x x $\frac{3x}{2}$Rate for carpeting = Tk. 5 per sq.m

Thus, total carpeting area of the room= ( $\frac{\text{total cost of carpeting}}{rate}$)= $\frac{270}{5}$ sq m = 54 sq m

Now, the area of the room, => x x $\frac{3x}{2}$ = $\frac{3x^{2}}{2}$ =54

=> x = 6

So, Length = $\frac{3}{2}$x6 = 9 m

Similarly, papered am will be = $\frac{\text{total expense}}{cost}$ =$\frac{1720}{10}$ = 172

Given, Area of one door and 2 windows = 8 sq m

Total area of 4 walls = Papered Area + Doors and Windows=172+8=1805qm.

Now, Total area of 4 walls = 180m=2 (length + breadth) x Height

=>2(9 +6) x h= 180m

=>h = 6m

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