Question

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

Answer 1

From the question,

Length of the room = 15 m

Width of the carpet = 75 cm = (75/100)m = 0.75 m

Cost of carpet = ₹ 80

Cost of carpeting the room = ₹ 19200

Let the length of the carpet be x m

∴Cost of x m carpet = ₹ (80 × x) = ₹ 80x

Then,

Cost of carpeting the room = ₹ 19200

= 80x = 19200

= x = 19200/80

= x = 240

∴The length of the carpet required for carpeting the room is 240m

Then,

Area of the carpet required for carpeting the room = Length of the carpet × Width of the carpet

= (240 × 0.75) m²

= 180m²

Now,

We have to find width of the room be b m.

Carpeting area = 15 m × b m

= 15b m²

∴ 15b m² = 180 m²

= b = (180/15) m

= b = 12 m

Hence, the width of the room is 12 m