Question

A piece of cloth costs Rs. $200$ per metre. If the piece was $5$m 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 the original rate per metre?

• A. $40$m and Rs. $15$
• B. $20$m and Rs. $10$
• C. $15$m and Rs. $5$
• D. None of the above

Answer 1

The correct option is B $20$m and Rs. $10$

Let the length of the piece be $x$ metres

Since the cost of $x$ metres cloth = Rs. $200$

$\therefore$ Cost of one metre cloth = Rs. $\frac{200}{x}$

New length of cloth = $(x+5)$ m

New cost of each metre of cloth = Rs. $\frac{200}{x+5}$

As per the given condition, $\frac{200}{x}-\frac{200}{x+5}=2$

$100(x+5)-100x=2$

$x^2+5x-500=0$

$(x+25)(x-20)=0$

$\therefore x=20$m

Original rate per metre = Rs. $\frac{200}{20}=$ Rs. $10$