Question

The total cost of a certain length of a piece of cloth
is rs.200. If the piece was 5 m longer and each metre
of cloth costs 2 less, the cost of the piece would have remained unchanged. How long is the piece
and what is its original rate per metre? ​

Answer 1

Answer:

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Answer 2

Let us assume length of the cloth to be x

The cost of cloth to be y per m.

Then

According to given data

x * y = 200

Therefore, y = 200/x ….(1)

Also given that if the piece were 5m longer then each metre of cloth would cost Rs2 less,

Then arranging the equation we get,

(x+5)(y -2) = 200

xy -2x + 5y -10 = 200

substituting the the value of y from equation 1 we get,

x(200/x) – 2x + 5(200 / X) – 10 = 200

1000/x – 2x = 200 – 190

1000 -2x2= 10x

500 -x2= 5x

x2+5x – 500 = 0

(x-20) (x+25) = 0

so, x= 20

x= -25 so will ignore this value

so, y = 200/x = 200/20 = 10

Hence, the length of the piece of cloth is 20 m and rate per metre is Rs 10.