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?

The total cost of a certain length of cloth is `Rs 200`. If the piece

1.	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?
Answer» 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`