#### Question

A piece of cloth costs Rs. 35. If the piece were 4 m longer and each meter costs Rs. one less, the cost would remain unchanged. How long is the piece?

#### Solution

Let the length of the piece be *x* metres.

Then, rate per metre = 35/x

According to question, new length = (x + 4) meters.

Since the cost remain same. Therefore, new rate per metre `=35/(x+4)`

It is given that

`35/x+35/(x+4)=1`

`(35(x+4)-35x)/(x(x+4))=1`

`(35x+140-35x)/(x^2+4x)=1`

`140/(x^2+4x)=1`

140 = x^{2} + 4x

x^{2} + 4x - 140 = 0

x^{2} + 14x - 10x - 140 = 0

x(x + 14) - 10(x + 14) = 0

(x + 14)(x - 10) = 0

x + 14 = 0

x = -14

Or

x - 10 = 0

x = 10

Because *x *cannot be negative.

Thus,* x = 10 *is the require solution.

Therefore, the length of the piece be x = 10 meters.

Is there an error in this question or solution?

#### APPEARS IN

Solution A Piece of Cloth Costs Rs. 35. If the Piece Were 4 M Longer and Each Meter Costs Rs. One Less, the Cost Would Remain Unchanged. How Long is the Piece? Concept: Solutions of Quadratic Equations by Factorization.