Question

The price of a lengthy clothe is Rs. 440. If the length of the cloth is increased by 1 metre then rate of cost becomes less Rs. 4 but the total cost price remain same.How long is the cloth ?​

Answer 1

Answer:

176m will be the total measure of the total long cloth.

Answer 2

The length of the cloth is 10 m.

Step-by-step explanation:

The price of the lengthy clothe = Rs. 440

Let the length of the piece of cloth be “x” metres then the new length of the piece of  cloth will be “(x + 1)” meters.  

So, the rate of cost per meter will be = Rs. [$\frac{440}{x}$]

And,

The new rate of cost per meter will be = Rs. [$\frac{440}{x+1}$]

According to the question, the total cost remains the same, so we can write eq. as,  

$\frac{440}{x}$ - 4 = $\frac{440}{x+1}$

⇒ $\frac{440}{x} - \frac{440}{x+1}$ = 4

⇒ $440 [\frac{1}{x} + \frac{1}{x+1}] = 4$

⇒ $110 [\frac{x+1-x}{x(x+1)}] = 1$

⇒ 110 = x² + x

⇒ x² + x – 110 = 0  

⇒ x² + 11x – 10x – 110 = 0

⇒ x(x + 11) - 10(x + 11) = 0

⇒ (x + 11) (x - 10) = 0

⇒ x = - 14  or x = 10

Neglecting the negative value

⇒ x = 10 m

Thus, the length of the piece of cloth is 10 m.

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Also View:

A piece of cloth costs Rs 35. If the piece were 4m longer and each metre costs Rs. one less, the cost would have remail unchanged. How lond is the piece?

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