Correct option is A. $$6 \,m$$
Because,
From the question,
Total cost of carpenting $$ = Rs. 6000$$
Rate of carpenting $$= Rs. 50$$ per meter
Then,
Length of the carpet $$= (6000 / 50) = 120 \,m$$
$$\therefore$$ Area of the carpet $$= (120 \times (75 / 100)) = 90 \,m^2$$
Area of the floor = Area of the carpet $$= 90 \,m^2$$
Hence, the width of the room = (Area / length)
$$= (90 / 15)$$
$$= 6 \,m$$