The total cost of a certain length of cloth is `Rs 200`. If the piece was 5 m longer and each metre of cloth costs `Rs2` less, the cost of the piece would have remained unchanged. How longer is the piece and what is its original rate per metre?

Explanation

Let, the length of the piece be x meters
Since the cost of x meters of cloth =RS.200
`implies` Cost of each meter of cloth `=RS.(200)/(x)`
New length of cloth =(x+5)m
New cost of each more of cloth `=RS.(200)/(x+5)`
Now, given `(200)/(x)-(200)/(x+5)=2`
`implies(200)/(x)-(200)/(x+5)=2implies(200x+1000-200x)/(x^(2)+5x)=2`
`1000=2x^(2)+10x`
`implies2x^(2)+10x-1000=0`
`x^(2)+5x+500=0`
`x^(2)+25x-20x-500=0`
`impliesx(x+25)-20(x+25)=0`
`implies(x-20)(x+25)=0`
`impliesx=20orx=-25`
Since, length cannot be negative
Hence, x=20m
and the original rate per metre `=RS.(200)/(20)=RS.10`