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?

• A. 10,20
• B. 20,10
• C. 30,20
• D. 20,30

Answer 1

The correct option is

B

20,10

Let the length of the cloth $=xm$ and its cost be $y$ rs.

Then Rate will be,

$xy=200\Rightarrow y=\frac{200}{x}.....\left(i\right)$

According to the question-
$(x+5)(y-2)=200$
Put the value from equation (1), we get

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

Solving this we get,

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

Or $x^2+25x-20x-500=0$

$(x-20)(x+25)=0$
So, $x=20m$ or $x=-25m$ (Not possible)

So, $x=20m$

Putting value of $x$ in equation (1) we get,

$y=\frac{200}{20}=Rs10$
Hence, the cloth is $20m$ long and price of cloth per meter is $Rs.10$