Question

A piece of cloth costs rupees $75$. If the piece is four meters longer and each meter costs rupees $5$ less, the cost remains unchanged. What is the length of the piece?

• A. $12$ meters
• B. $8$ meters
• C. $10$ meters
• D. $6$ meters

Answer 1

Answer: (D)

$6$ meters

According to question,
Let the length of piece of cloth be x
Let the rate per meter be y
$\therefore$ xy$=75$
$x=\frac{75}{y}$
Again, $4$ meters longer and Rs. $5$ less
Then,
$(x+4)(y-5)=75$
$(x+4)(y-5)=xy$
$xy-5x+4y-20=xy$
$4y-5x=20$
$4y-5\times \frac{75}{y}=20$
$\Rightarrow 4y^2-20y-375=0$
By solving,
we get $y=12.5$
Rate per meter $=12.5$
Price of cloth $=75$
$\therefore$ Length of cloth $=\frac{75}{12.5}=6$ meters.