LEVEL-1 1. A piece of cloth costs 35. If the piece were 4 m longer and each metre costs one less, the cost would remain unchanged.

Question

LEVEL-1
1. A piece of cloth costs 35. If the piece were 4 m longer and each metre costs one less, the
cost would remain unchanged. How long is the piece?​

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Autumn 1 month 2021-08-19T22:36:12+00:00 1 Answer 0 views 0

Answers ( )

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    2021-08-19T22:37:15+00:00

    Answer :

    10m

    Step-by-step explanation:

    Let the length of the cloth be x .

    It is given that the cloth costs ₹35 .

    ⇒ cost of 1 m cloth is 35/x .

    Now the given condition is that length of cloth is 4m more .

    ⇒ new length =x+4 .

    Next condition is cost of each /1m is 1 less

    ⇒ new cost of 1m = 35/x-1 .

    and it also says that the price remains unchanged  .

    new cost of 1m × new length of cloth = total cost

    ⇒ (35/x – 1)(x + 4 ) = ₹ 35

    ⇒ (35-x)(x+4)=35×x

    ⇒ 35x + 140 -x² -4x = 35x

    ⇒ x² +4x -140 =0

    ⇒ x² +14x – 10x -140 =0

    ⇒ x( x+14 ) -10( x +14 ) =0

    ⇒ (x +14) ( x – 10 ) =0

    ⇒ x=-14 , x=10 .

    But x= length and can’t be negative  .

    ⇒ x = 10m .

    ∴ The length of the cloth is 10 m  .

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