A piece of cloth costs Rs 300 If the piece were 5m longer and each metre of cloth - Maths - Quadratic Equations

Question

A piece of cloth costs Rs 300 If the piece were 5m longer and
each metre of cloth costed Rs 2 less, the cost of the piece would
have remained unchanged How long is the piece and what is its
original cost per metre?

ramandeep.singh · Accepted Answer

Let length of cloth be l metres and p be the price per metre.

Therefore, according to the question,

$l \times p = 300 \Rightarrow l = \frac{300}{p} ........ (1)$

Now,

$(l + 5) (p - 2) = 300$

Using equation (1), we get

$(\frac{300}{p} + 5) (p - 2) = 300 \Rightarrow 300 - \frac{600}{p} + 5 p - 10 = 300 \Rightarrow 5 p^{2} - 10 p - 600 = 0 \Rightarrow p^{2} - 2 p - 120 = 0 \Rightarrow (p - 12) (p + 10) = 0 ∴ p - 12 = 0 o r p + 10 = 0 \Rightarrow p = 12 o r p = - 10$

As price can't have a negative value, therefore, we neglect the value p = -10.

$∴ p = R s 12$

Putting this value in equation (1), we get

$l = \frac{300}{12} = 25 m$

Thus, length of cloth = 25 m

Price = Rs 12 / metre

A piece of cloth costs Rs. 300. If the piece were 5m longer and each metre of cloth costed Rs.2 less, the cost of the piece would have remained unchanged. How long is the piece and what is its original cost per metre?