Given length of the room = 15m

Width of the carpet = 75 cm = 75/100 m = 3/4 m     (since 100 cm = 1 m. So 75 cm = 75/100 m)

Let length of the carpet is L.

Given cost of the carpet per meter = 80 rupees

Cost of the carpet required for the room = 80*L

Again given that total cost of the carpeting = 19200

So 80*L = 19200

=> L = 19200/80

=> L = 240 m

Now area of the carpet required for the room = Length *breadth

                                                                     =   3/4 * 240

                                                                     = 3* 60

                                                                     = 180 m²

Now let width of the room is b.

Area of the room = 15*b m²

So 15*b = 180

=> b = 180/15

=> b = 12

So width of the room is 12 m