Question

Length of a room is twice its height and its breadth is $1\frac{1}{2}$ times its height$.$ The cost of white washing the walls at the rate of $32Rs$ per sq. m is $3584Rs.$ Find the cost of tiling the floor of the room at $135Rs$ per sq. m$.$

• A. $6480Rs$
• B. $6400Rs$
• C. $6450Rs$
• D. $6580Rs$

Answer 1

The correct option is A $6480Rs$

Let the height $=h$. Then Length of wall $=2h$ and breadth $=1\frac{1}{2}h$.
Cost of white washing wall $=Rs3584.$
Area of wall white washed $=\frac{Costofwhitewashingwall}{rateofwhitewashingpersq.m}=\frac{3584}{32}=112m^2$
Area of wall of a room is lateral surface area of a cuboid
Then, $2h(l+b)=112$
$or,2h(2h+\frac{3}{2}h)=112or,2h\left(\frac{7h}{2}\right)=112or,7h^2=112or,h^2=16orh=4.$
Height of cuboid$=h=4m$
Length of cuboid$=2h=8m$
Breadth of cuboid$=\frac{3}{2}h=6m$
Area of floor $=l\times b$
$=8\times 6=48m^2$
Cost of tiling the floor at Rs.135 per sq. m $=135\times 48=Rs.6480$