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 ?​

Answer 1

Information given to us:

• Cost of a piece of cloth is Rs.200
• If it's piece of cloth was 5m longer then each metre of cloth cost would be Rs.2 less.

What we have to calculate:

• Length of piece and original rate per metre?

Let us assume:

• Length of piece be y metre

Finding out cost of one metre of cloth:

• Rs. 200/y

_________

As the piece was 5m long:

• So length of cloth would be, finding out new length of cloth:

➝ (y + 5) m

Finding out new cost of each metre of cloth:

➝ 200 / (y+5)

Thus, new cost would be Rs. 200 / (y+5)

Subtracting both the costs:

Here we subtracting both the costs which is new cost and the previous cost the cloth. It would be equal to Rs.2.

➝ 200/y - 200/y+5 = 2

Taking L.CM.,

➝ 200/y + 1000 - 200/ y(y+5) = 2

Now,

➝ 200/y + 1000 - 200/ y²+5y = 2

On subtracting 200/y with 200/y we get,

➝ 1000 / y²+5y = 2

Atq,

➝ 1000 = 2(y²+5y)

➝ 1000/2 = y²+5y

➝ 500 = y²+5y

Reversing the side 500 would be negative,

➝ y² + 5y - 500 = 0

Forming factors,

➝ y² + 25y - 20y - 500

Grouping terms,

➝ y(y + 25) - 20(y + 25)

➝ (y + 25) (y - 20)

Now, comparing both which would be correct:

➝ y would be 20 as -25 can't be accepted as length can never be negative.

Conclusion:

• Piece is 20m long.

Finding out original rate:

➝ Cost of cloth / length of piece

➝ 200/20

➝ 20/2

➝ 10

• Original rate per metre is Rs.10