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 the length of the cable = L meters
the cost of the cable =  200 / L  Rs/meter

given  ( L + 3) * (200/L  -  2) = Rs 200
           200 - 2 L + 600/L - 6 = 200
simplifying
           L² + 3 L - 300 = 0

           L =  [-3 +- √1209] /2 =  15.885  meters
           cost of the cable = 12.59 Rs/m
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in terms of the cost of the cable:

Let the cost of the cable be :  C  Rs/m
So length of the given cable:    200 / C

given:    (200 / C + 3) (C - 2) = 200
             200 - 400 / C  + 3 C - 6 = 200
             3 C² - 6 C - 400 = 0

Answer 2

let the length of the cable = x meters
the cost of the cable =  200 / x  Rs/meter

given  ( x + 3) * (200/x  -  2) = Rs 200
           200 - 2 x + 600/x - 6 = 200
by simplifying
           x² + 3 L - 300 = 0 
           x =  [-3 +- √1209] /2 =  15.885  meters
           cost of the cable = 12.59 Rs/m
in terms of the cost of the cable:

Let the cost of the cable be :  C  Rs/m
So length of the given cable:    200 / C

given:    (200 / C + 3) (C - 2) = 200
             200 - 400 / C  + 3 C - 6 = 200
             3 C² - 6 C - 400 = 0