Question

An electric cable cost Rs 200.If the cable was 3m longer and each meter of cable costs 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 original length of cable be 'x'm
Total cost of 'x'm of cable = Rs. 200
Therefore cost of cable per meter = Rs. (200/x)

New length of cable = (x+3)m
New cost of cable per meter = (200/x)-2 = Rs. (200-2x)/x
Total cost remains the same i.e Rs. 200

Therefore, total cost = new cost per meter * new length of cable
=> 200 = (x+3)*(200-2x)/x
=> 200x = 200x-2x^2+600-6x
=> 0 = -2x^2-6x+600
Multiplying both sides with (-1)
=> 0 = 2x^2+6x-600

... is the required quadratic equation.On solving you get 15.885m and -18.885m (-ve value to be discarded.)