Question

A piece of cloth costs birr 200. If the piece was 5m longer, and the cost of each cloth was birr 2 less, the cost of the piece would have remained unchanged. How long is the piece and what is its original price per metre?

Answer 1

$\large\underline{\sf{Solution-}}$

Let assume that the length of the cloth be 'x' meter.

Amount to be paid = birr 200

So, Cost of per meter length is

$\rm \:  =  \:  \: \dfrac{200}{x}$

Again,

Length of cloth = x + 5 meter

Amount to be paid = birr 200

So, Cost of per meter length is

$\rm \:  =  \:  \: \dfrac{200}{x + 5}$

According to statement,

$\rm :\longmapsto\:\dfrac{200}{x} - \dfrac{200}{x + 5} = 2$

$\rm :\longmapsto\:\dfrac{200(x + 5) - 200x}{x(x + 5)} = 2$

$\rm :\longmapsto\:\dfrac{200x + 1000 - 200x}{x(x + 5)} = 2$

$\rm :\longmapsto\:\dfrac{1000}{x(x + 5)} = 2$

$\rm :\longmapsto\:\dfrac{500}{x(x + 5)} = 1$

$\rm :\longmapsto\: {x}^{2} + 5x = 500$

$\rm :\longmapsto\: {x}^{2} + 5x - 500 = 0$

$\rm :\longmapsto\: {x}^{2} + 25x - 20x - 500 = 0$

$\rm :\longmapsto\:x(x + 25) - 20(x + 25) = 0$

$\rm :\longmapsto\:(x + 25)(x - 20) = 0$

$\rm :\longmapsto\:x = 20 \: \: or \: \: - 25 \: \: (rejected)$

So,

Length of cloth is 20 meter

and

Cost per meter = birr 10.