Question

A piece of cloth costs $Rs.200.$If the piece was $5m$longer and each meter 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 meter $?$

Answer 1

Determine the original rate per meter:

Let the length of the cloth be $x\mathrm{m}$.
Cost per meter $=₹\frac{200}{\mathrm{x}}$
The new length of the cloth $=(\mathrm{x}+5)\mathrm{m}$
The new cost per meter $=₹\left(\frac{200}{\mathrm{x}}-2\right)$
$(\mathrm{x}+5)\left(\frac{200}{\mathrm{x}}-2\right)=200$

$\frac{(\mathrm{x}+5)(200-2\mathrm{x})}{\mathrm{x}}=200$

or $200\mathrm{x}-2{\mathrm{x}}^2+1000-10\mathrm{x}=200\mathrm{x}$

or ${\mathrm{x}}^2+5\mathrm{x}-500=0$

or $(\mathrm{x}+25)(\mathrm{x}-20)=0$

or $\mathrm{x}\ne -25,\therefore \mathrm{x}=20$

Length of the piece $=20\mathrm{m}$.
Original cost per meter $=$ Rs.$\frac{200}{20}=$ Rs. $10$.

Hence, length of the piece is $20\mathrm{m}$ and original cost per meter is Rs. $10$.