Question

an electric cable cost Rs-200.If cable was 5 mtrs longer and each meter of cable cost Rs-2 less the cost of cable would have remained unchanged.represent the above situation in the form of a quadratic equation

Answer 1

Let the length of piece of clot be x

So, cost of x m cloth = Rs 200 => cost of 1m cloth = Rs 200/x (i)

Now, the piece is 5 m long

New length = (x + 5) m

Also given is that if the cost is reduced by Rs 2 per m, the overall price of the piece of cloth will remain unaffected.

So, the price each m = Rs (200/x+5) - 2 (ii)

Since (i) = (ii) which is given

200/x = (200/x+5) - 2

=> 200/x = (200 - 2x - 10)/x + 5

=> 200/x = 190 - 2x/x + 5

=> 200x + 1000 = 190x - 2x2

=> 2x2 + 10x + 1000 = 0

=> x2 + 5x + 500 = 0

=> x2 - 20x + 25x + 500 = 0

=> x(x - 20) + 25 (x - 20) = 0

=> (x - 20) (x + 25) = 0

=> x = 20 or - 25

But length of the cloth cannot be in negative

So, x ie. length of cloth = 20m