Question:
An electric cable cost Rs.200. If the cable was 3 metres longer and each metre 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:
Let the length of the cable is x m.
Cost of the cable = Rs (200/x) per m.
Given, If the cable was 3 metres longer and each metre of cable cost Rs.2 less,
the cost of cable would have remained unchanged
=> (x + 3) * (200/x - 2) = 200
=> x(200/x) - 2x + 3(200/x) - 6 = 200
=> 200 - 2x + 600/x - 6 = 200
=> -2x + 600/x - 6 = 0
=> 2x - 600/x + 6 = 0
=> (2x2 - 600 + 6x)/x = 0
=> 2x2 + 6x - 600 = 0
=> 2(x2 + 3x - 300) = 0
=> x2 + 3x - 300 = 0
This is the required equation.
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