The cost of papering the four walls of a room at 75 paise per square metre is ₹ 240. The height of the room is 5 metres. Find the length and the breadth of the room, if they are in the ratio 5 : 3.

Given:

Total cost = ₹ 240

Cost of papering = 75 paise per sq. m. = ₹ 0.75 per sq. m.

Height of the room = 5 m

Ratio of length to breadth = 5 : 3

Let the length and breadth of room be 5a and 3a.

Area of the four walls = 2(l + b)h

= 2(5a + 3a)5

= 2 x 8a x 5 sq. m.

= 80a sq. m.

Total cost = Area of the four walls x Cost of papering

⇒ 240 = 80a x 0.75

⇒ 240 = 60a

⇒ a = $\dfrac{240}{60}$

⇒ a = 4 m

The length and breadth of room are 5a and 3a = 5 x 4 m and 3 x 4 m

= 20 m and 12 m

Hence, the length and breadth of the room are 20 m and 12 m, respectively.