A room is 16 m long and 13.5 m broad.

As, the area of the floor $=$ length $\times$ breadth

$=16 \times 13.5$

$=216 \mathrm{~m}^{2}$

And, the width of the carpet $=75 \mathrm{~m}$

So, the length of the carpet required $=\frac{\text { Area of the floor }}{\text { Width of the carpet }}$

$=\frac{216}{75}$

$=2.88 \mathrm{~m}$

Now, the cost of the carpet required $=2.88 \times 60=₹ 172.80$

Hence, the cost of covering the floor with carpet is ₹172.80.

Disclaimer: The answer given in the textbook is incorrect. The same has been rectified above.