The length and breadth of a hall are in the ratio 4: 3 and its height is 5.5 meters.
Question:

The length and breadth of a hall are in the ratio 4: 3 and its height is 5.5 meters. The cost of decorating its walls (including doors and windows) at Rs 6.60 per square meter is Rs 5082. Find the length and breadth of the room.

Solution:

Let the length be 4a and breadth be 3a

Height = 5.5m [Given]

As mentioned in the question, the cost of decorating 4 walls at the rate of Rs. 6.60 per m2 is Rs. 5082.

Area of four walls * rate = Total cost of Painting

2(l + b) * h * 6.6 = 5082

2(4a + 3a) * 5.5 * 6.6 = 5082

$7 a=\frac{5082}{2 * 5.5 * 6.6}$

7a = 70

a = 70/7

a = 10

Length = 4a = 4*10 = 40 m

Breadth = 3a = 3*10 = 30 m