Question

A piece of cloth costs birr 200. If the piece was 5m longer, and the cost of each cloth was birr 2 less, the cost of the piece would have remained unchanged. How long is the piece and what is its original price per metre?

Answer 1

Let the length of the piece be x metres. Then, rate per metre =Rs.

x

200

New length =(x+5) metres

Since the cost remains same

New rate per metre =Rs.

x+5

200

It is given that

x

200

−

x+5

200

=2

⇒

x(x+5)

200(x+5)−200x

=2⇒

x(x+5)

1000

=2

⇒x

2

+5x=500⇒x

2

+5x−500=0$

⇒x

2

+25x−20x−500=0

⇒(x+25)(x−20)=0⇒x+25=0

orx−20=0⇒x=20orx=−25

But x cannot be negative. So, x=20

Rate per metre Rs.

x

200

=Rs

20

200

=Rs.10

Hence the length of the piece of cloth is 20 meters and rate =Rs. 10 per meter