Question

Manav is painting a rectangular room and the dimension of this room are given by X Y and Z feat Manan takes 8 hour to paint a wall with dimension X and Z he takes 4 hours to paint a wall with dimension Y and Z and 12 hour 2.10 the selling which has dimension X and Y Manu works at a constant rate X equal 6 what is the value of the room?​

Answer 1

Answer:

B) 36 cubic feet

Step-by-step explanation:

Dimensions of the room are x, y and z feet. It is given that x = 6 feet.

Manav took 8 hours to paint the wall with dimensions x and z.

This means, in 8 hours Manav painted area = xz = 6z

In 1 hour Manav painted area = 6z/8

Manav took 4 hours to paint the wall with dimensions y and z.

This means, in 4 hours Manav painted area = yz

In 1 hour Manav painted area = yz/4

Manav took 12 hours to paint the ceiling with dimensions x and y.

This means, in 12 hours Manav painted area = xy = 6y

$In \: 1 \: hour \: Manav \: painted \: the \: area = \frac{6y}{12}=\frac{y}{2}$

Since, Manav works at constant rate, this means the worked done in 1 hour in all 3 cases would be the same. So we can write:

$\frac{6z}{8}=\frac{yz}{4}=\frac{y}{2}$

Using the first two equations, we get:

$\begin{gathered}{6z}{8}=\frac{yz}{4}\\\\ \frac{6}{8}=\frac{y}{4}\\\\ y=\frac{6}{8} \times 4\\\\ y = 3\end{gathered}$

Using the last two equations, we get:

$\begin{gathered}\frac{yz}{4}=\frac{y}{2}\\\\ \frac{z}{4}=\frac{1}{2}\\\\z=2\end{gathered}$

So, we have the follwoing dimensions of the room:

x = 6 feet

y = 3 feet

z = 2 feet

So the volume of the room is = 6 x 3 x 2 = 36 cubic feet