Question

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

Answer 1

Solution :-

Let the cost of x m cloth be Rs 200.
Cost of 1 m cloth = Rs 200/x

According to the question,

=> (x + 5) (200/x - 2) = 200
=> (x + 5) {(200 - 2x)/x} = 200
=> (x + 5) (200 - 2x) = 200x
=> 200x - 2x² + 1000 - 10x = 200x
=> 2x² + 10x - 1000 = 0
=> 2(x² + 5x - 500) = 0
=> x² + 25x - 20x - 500 = 0
=> x(x + 25) - 20(x + 25) = 0
=> (x - 20) (x + 25) = 0
=> x = 20 or x = - 25

x ≠ - 25 (Because length can't be negative)


Therefore,
Total length of cloth = 20 m
Cost of 1 m of cloth = Rs 200/20 = Rs 10

Answer 2

Answer:

Step-by-step explanation:

Solution :-

Let the length of cloth be x cm.

Then, cost per metre = Rs. 200/x

Again, new length of the cloth = (x + 5) m

Then, new cost per metre = Rs. (200/x - 2)

According to the Question,

⇒ (x + 5) [(200/x) - 2] = 200

⇒ (x + 5)(200 - 2x)/x = 200

⇒ 200x - 2x² + 1000 - 10x = 200x

⇒ x² + 5x - 500 = 0

⇒ x² + 25x - 20x - 500 = 0

⇒ x(x + 25) - 20(x + 25) = 0

⇒ (x + 25) (x - 20) = 0

⇒ x = - 25, 20 (As x can't be negative)

⇒ x = 20

Hence, Length of the piece is 20 m.

Original cost per metre = 200/20 = Rs. 10

Hence, the Original cost per metre is Rs. 10.