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A piece of cloth costs Rs 200. If the piece was $5 m$ longer and each meter of cloth cost 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 ?

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20m , Rs. 10

30m , Rs. 10

20m , Rs. 20

10m , Rs. 10

answer is A.

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Detailed Solution

Given that,
A piece of cloth costs Rs 200. If the piece was

5 m

longer and each meter of cloth cost Rs 2 less, the cost of the piece would have remained unchanged.
Let the length of the piece be x times then the rate per meter will be

R s . 200 x

.
Now, according to the question,

200 x − 200 x + 5 = 2 ⇒ 200 x + 5 − 200 x x x + 5 = 2 ⇒ 1000 x x + 5 = 2 ⇒ x 2 + 5 x − 500 = 0

On simplifying,

x 2 + 5 x − 500 = 0 ⇒ x + 25 x − 20 = 0 ⇒ x = 20, x = − 25

The negative value of x is not possible because length cannot be negative.
Now, the rate will be

R s . 20020 = R s .10

.
Therefore, the length of the piece of cloth is 20m and the rate is Rs.10.
Hence, option 1 is correct.

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