Answer:
=Rs.10
Explanation:
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A piece of cloth costs Rs. 200. If the piece was 5m longer and each meter of cloth costs Rs. 2 less the cost of the piece would have remained unchanged. How long is the piece and what is the original rate per meter?
Medium
Solution
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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