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A piece of cloth costs Rs. 35. If the piece were 4 m longer and each meter costs Rs. 1 less, the cost would remain unchanged. How long is the piece?

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10m

20m

30m

40m

answer is A.

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Detailed Solution

Given that a piece of cloth costs Rs. 35.
If the piece were 4 m longer and each meter costs Rs. 1 less, the cost would remain unchanged.
Assume that the piece of cloth costing Rs. 35 be x meters in length.

Therefore the cost per metre will be = Rs . 35 x

Obtain the same cost if the cost per meter is decreased by a rupee and the length of the original cloth is increased by 4 meters.
Therefore,

35 x − 1 (x + 4) = 35 ⇒ (35 − x) (x + 4) x = 35 ⇒ 35 x + 140 − x 2 − 4 x = 35 x ⇒ x 2 + 4 x − 140 = 0

⇒ x 2 + 14 x − 10 x − 140 = 0 ⇒ x (x + 14) − 10 (x + 14) = 0 ⇒ (x − 10) (x + 14) = 0

⇒

x - 10 = 0

x + 14 = 0

⇒

x = 10, - 14

But the length can never be negative, hence the length of the original piece of cloth is 10m.
Hence, the correct option is 1.

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