Question

The total cost of a certain length of a piece of cloth is Rs 200. If the piece was 5 cm 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 its original rate per metre?

Answer 1

Case 1 : Let here be xm of cloth initially.
Cost of xm cloth =Rs 200
$\Rightarrow$ of 1m initially =Rs $\frac{200}{x}$
Case 2: Piece is 5m longer, i.e. x +5 m
cost/meter is Rs 2 less i.e. Rs $\frac{200}{x}-2$
Total price =(x+5) $(\frac{200}{x}-2)=200$ (Given that total price is unchanged)
$(x+5)(\frac{200}{x}-2)=200x\left(\frac{200}{x}\right)-2x+\frac{5\times 200}{x}-5\times 2=200200-2x+\frac{1000}{x}-10=200190+\frac{1000}{x}-2x=200\frac{1000}{x}-2x=10\frac{500}{x}-x=5500-x^2=5x{x}^2+5x-500=0$
$x^2+25x-20x-500=0x(x+25)-20(x+25)=0(x-20)(x+25)=0x=20,-25$
Length cannot be -ve, i.e. length 15 20 m
cost/meter originrally =$\frac{200}{x}=\frac{200}{20}=Rs10$