Question

A piece of cloth cost Rs 200 If the piece were 5mlonger and each metre of cloth costs Rs 2 less the cost of the piece would have remain unchanged. How long is the piece and what is its original rate per metre? ​

Answer 1

Answer:

length of the cloth is 20 m and rate = rupees 10 per metre

Step-by-step explanation:

Let the length of the cloth be x metres and rate per metre be ₹200/x.

New length =(x+5) metres

therefore, New rate per metre = 200/x+5

$\frac{200}{x} - \frac{200}{x + 5} = 2$

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

$\frac{200x + 1000 - 200x}{x(x + 5)} = 2$

$cancelling \: 200x \: and - 200x$

$\frac{1000}{x(x + 5)} = 2$

$\frac{1000}{ {x}^{2} + 5x } = 2$

$1000 = 2 {x}^{2} + 10x$

$dividing \: both \: sides \: with \: 2$

$we \: get$

${x}^{2} + 5x = 500$

${x}^{2} + 5x - 500 = 0$

$factorisation \: by \: splitting \: the \: middle \: term$

${x}^{2} + 25x - 20x - 500 = 0$

$(x + 25)(x - 20) = 0$

$x + 25 = 0$

$x = - 25$

$x - 20 = 0$

$x = 20$

$x \: cannot \: be \: negative \: so$

$x = 20$

$rate \: per \: metre = rupees \: \frac{200}{x} = \frac{200}{20} = 10$