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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 Rs. 2 less, the cost of the piece would have remained unchanged. How long is the piece and what is its original rate per metre?

 

Answers (1)

Let the length of cloth = x.

Cost of cloth per m = y.

\mathrm{xy = 200\Rightarrow y = \frac{200}{x}\qquad -(i)}

Conditions- If the piece were 5m longer and each metre of cloth cost Rs. 2 less.

        \mathrm{(x + 5)(y-2) = 200\qquad -(ii)}

        \mathrm{xy -2x + 5y - 10 = 200}

Put value of y from eq(i) in eq(ii)

        \mathrm{(x + 5)\left(\frac{200}{x} - 2 \right ) = 200}

        \mathrm{\frac{(x+5)(200-2x)}{x} = 200}

or,    \mathrm{200x - 2x^2 + 1000 -10x = 200x}

or,    \mathrm{x^2 +5x -500 = 0}

or,    \mathrm{(x + 25)(x-20) = 0}

        \mathrm{x \neq -25 \quad \therefore x = 20}

        \mathrm{y = \frac{200}{x} = 10}

Length of the piece = 20m

Original cost per metre \mathrm{=\frac{Rs. \ 200}{20} = Rs. \ 10}

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Safeer PP

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