Question

The total cost of a certain length of a peice of cloth is rupees 200 . If the piece was 5 m longer and each meter of cloth costs rupees 2 less, the cost of the piece would have remained unchanged . How long is the piece and what is its original rate per meter?

Answer 1

let the certain length be x therefore xm=200 rupees

if each meter cost rupees 2,for 5m is rupees 10

the length of the cloth 200*5/10=100m

and the original rate is 200/100=rupees 2

Answer 2

$\Large{\textbf{\underline{\underline{According\;to\;the\;Question}}}}$

Assumption,

Length of cloth = p

So,

Cost = 200/p

Now,

Length of cloth (New) = (p + 5)

So,

Cost = (200/p - 2)

Situation,

(p + 5) [(200/p) - 2] = 200

(p + 5)(200 - 2p)/p = 200

200p - 2p² + 1000 - 10p = 200p

p² + 5p - 500 = 0

p² + 25p - 20p - 500 = 0

p(p + 25) - 20(p + 25) = 0

(p + 25)(p - 20) = 0

p = - 25, 20 (Negative value is not applicable)

p = 20

Therefore,

Length of piece = 20 m.

Original cost :-

= 200/20

= Rs. 10 per m