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.

Dear Student!

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 80*x* 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 m^{2}

Let the width of room be *b* m.

Area to be carpeted in the room = 15 m × *b* m = 15 *b* m^{2}

∴ 15*b* m^{2} = 180 m^{2}

Thus, the width is room is 12 m.

Cheers!

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