# The cost of painting the four walls of a room 12 m long at ₹30 per m2 is ₹7560 and the cost of covering the floor with mat at ₹25 per m2 is ₹2700.

Question:

The cost of painting the four walls of a room 12 m long at 30 per m2 is 7560 and the cost of covering the floor with mat at 25 per m2 is 2700. Find the dimensions of the room.

Solution:

As, the rate of covering the floor $=₹ 25$ per $\mathrm{m}^{2}$

And, the cost of covering the floor $=₹ 2700$

So, the area of the floor $=\frac{2700}{25}$

$\Rightarrow$ length $\times$ breadth $=108$

$\Rightarrow 12 \times$ breadth $=108$

$\Rightarrow$ breadth $=\frac{108}{12}$

$\therefore$ breadth $=9 \mathrm{~m}$

Also,

As, the rate of painting the four walls $=₹ 30$ per $\mathrm{m}^{2}$

And, the cost of painting the four walls $=₹ 7560$

So, the area of the four walls $=\frac{7560}{30}$

$\Rightarrow 2$ (length $+$ breadth)height $=252$

$\Rightarrow 2(12+9)$ height $=252$

$\Rightarrow 2(21)$ height $=252$

$\Rightarrow 42 \times$ height $=252$

$\Rightarrow$ height $=\frac{252}{42}$

$\therefore$ height $=6 \mathrm{~m}$

So, the dimensions of the room are $12 \mathrm{~m} \times 9 \mathrm{~m} \times 6 \mathrm{~m}$.