Question

A piece of cloth costs Rs. 35. If the piece were 4 m longer and each meter costs Rs. 1 less, the cost would remain unchanged. How long is the piece?

Answer 1

Let the length of the piece be x metres.

Then, rate per metre = `35/x`

According to question, new length = (x + 4) meters.

Since the cost remain same. Therefore, new rate per metre `=35/(x+4)`

It is given that

`35/x+35/(x+4)=1`

`(35(x+4)-35x)/(x(x+4))=1`

`(35x+140-35x)/(x^2+4x)=1`

 `140/(x^2+4x)=1`

140 = x² + 4x

x² + 4x − 140 = 0

x² + 14x − 10x − 140 = 0

x(x + 14) − 10(x + 14) = 0

(x + 14) (x − 10) = 0

x + 14 = 0

x = −14

Or

x − 10 = 0

x = 10

Because x cannot be negative.

Thus, x = 10 is the require solution.

Therefore, the length of the piece be x = 10 meters.