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.
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.