Question

A piece of cloth costs Rs 200. If the piece was 5m longer and each metre of cloth costs Rs 2 less, the cost of the piece would have remained unchanged. How long is the piece and what is the original rate per metre?
solve in notebook........................................................

Answer 1

Solutions :-

Let the length of a piece of cloth be x
And the original rate per metre be y

According to the question,

x × y = 200
=> xy = 200 _______(i)

(x + 5) × (y - 2) = 200
=> xy - 2x + 5y - 10 = 200 ________(ii)


Putting the value of xy in equation (ii) we get,

=> 200 - 2x + 5y - 10 = 200
=> - 2x + 5y = 10
=> y = (2x + 10)/5 ______(iii)


Putting the value of y in equation (i) we get,

=> x (2x + 10)/5 = 200
=> 2x² + 10x = 200 × 5
=> 2x² + 10x - 100 = 0
=> 2(x² + 5x - 500) = 0
=> x² + 5x - 500 = 0/2
=> x² + 25x - 20x - 500 = 0
=> x(x + 25) - 20(x + 25) = 0
=> (x + 25) (x - 20) = 0
=> x = - 25 or x = 20

Length of cloth be taken positively.

Putting the value of x in equation (iii) we get,

=> y = (2 × 20 + 10)/5
=> y = 50/5 = 10


Hence,
The length of a piece of cloth = 20 m
And The original rate per metre = Rs 10 per metre

Answer 2

Answer:

20 m & Rs. 10

Step By Step Explanation:

Let the length of the cloth be x m and the cost of the cloth per metre be Rs y.

Cost of the piece of cloth = Rs 200

∴ x × y = 200 .....(1)

∴ y = 200/x .....(2)

According To The Question:

(x + 5) (y - 2) = 200

∴ xy - 2x + 5y - 10 = 200

∴ 200 - 2x + 5 × 200/x - 10 = 200 [ From (1) & (2) ]

∴ - 2x² + 1000 - 10x = 0

⇒ x² + 5x - 500 = 0

∴ x² + 25x - 20x - 500 = 0

∴ x (x + 25) - 20 (x + 25) = 0

∴ (x - 20) (x + 25) = 0

⇒ (x - 20) = 0 or (x + 25) = 0

∴ x = 20 or x = - 25 ( Neglect )

Hence, The length of the cloth is 20 m and Cost of the cloth per metre is 200/20 = Rs 10.