The cost of papering four walls of a room at ₹ 14 per square metre is ₹ 3,150. The height of the room is 5 metres. Find the length and the breadth of the room, if they are in the ratio 4 : 1.

The length and the breadth of the room are in the ratio 4 : 1.

Let the length of the room be 4a and breadth of the room be a.

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

= 2(4a + a) x 5

= 10 x 5a

= 50a square metres

The cost of papering the four walls = Area of the walls x 14

⇒ 50a x 14 = 3,150

⇒ 50a = $\dfrac{3,150}{14}$

⇒ 50a = 225

⇒ a = $\dfrac{225}{50}$

⇒ a = 4.5

So, the length of the room = 4a = 4 x 4.5 = 18 m

And breadth of the room = 1a = 1 x 4.5 = 4.5 m

Hence, the length of the room is 18 m and the breadth of the room is 4.5 m.