Question

The length of a room is 1.5 times of its breadth. The cost of carpeting the at Rs. 5 per sq. m is Rs. 270 and the cost of papering the four walls at Rs. 10 per $m^2$ is Rs. 1720. If a door and 2 windows occupy 8 sq. m, find the height of the room.

• A. 9 m
• B. 4 m
• C. 6 m
• D. 8 m

Answer 1

The correct option is C

6 m

Let breadth = x m, length = $\frac{3x}{2}$ m and height = h m

Area of the floor = $\frac{totalcostofcarpeting}{rate}$

= $\frac{270}{5}$ sq m = 54 sq m

$\Rightarrow$ $x$ $\frac{3x}{2}$ = 54

$\Rightarrow$ $x^2$ = 54 $\left(\frac{2}{3}\right)$ = 36

$\Rightarrow$ x = 6 m

So breadth = 6 m and length= $\frac{3x}{2}$ $\times$ 6 = 9 m

Now papered area = $\frac{1720}{10}$ = 172 sq m

Area of one door and 2 windows =8 sq m

Total area of 4 walls = 172 + 8 = 180 sq m

$\Rightarrow$ 2 (9+6) h = 180

$\Rightarrow$ h = $\frac{180}{3}$ = 6 m

So, height of the room is 6 m.