Please give the solution and explain this problem.

The cost of carpeting a room 15 m long with a carpet of width 75 cm at Rs 80 per meter is Rs 19200. Find the width of the room.

Dear Student!

Given, Length of the room = 15 m

Width of the carpet = 75 cm =  ( 1m = 100 cm)

Let the length of the carpet required for carpeting the room be x m.

Given, Cost of carpet = Rs 80/ m

Cost of x m carpet = Rs × x m = Rs 80x m 

Given, Cost of carpeting the room = Rs 19200

∴ 80 x = 19200

⇒ x = 240.

So, the length of carpet required for carpeting the room is 240 m.

Area of carpet required for carpeting the room 

= Width of the carpet × Length of the carpet

= 180 m²

Let the width of room be  b m.

Area to be carpeted in the room = 15 m × b m = 15 b m²

∴ 15b m² = 180 m²

Thus, the width is room is 12 m.

Cheers!