Question

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

Answer 1

The total cost of cloth piece = Rs. 300
Let the length of the piece of cloth in the beginning = x m

Then cost of 1 metre = Rs. `(300)/x`

In second case, length of cloth = (x + 5)

Cost of 1 metre = Rs. `(300)/(x + 5)`
According to the condition,

`(300)/x - (300)/(x + 5)` = 2

⇒ `300(1/x - 1/(x + 5))` = 2

⇒ `300((x + 5 - x)/(x(x + 5)))` = 2

⇒ `(300 xx 5)/(x(x + 5))` = 2

⇒ `(150 xx 5)/(x(x + 5))` = 1 ...(Dividing by 2)

750 = x² + 5x
⇒ x² + 5x - 750 = 0
⇒ x² + 30x - 25x - 750 = 0
⇒ (x + 30) -25(x + 30) = 0
⇒ (x + 30)(x - 25) = 0
Either x + 30 = 0,
then x = -30
which is not possible being negative
or
x - 25 = 0,
then x = 25
∴  Length of cloth piece in the begining = 25 metres

and rate per metre = Rs. `(300)/(25)` = Rs. 12.