A journey of 600 km, Due to some problem in Vehicle speed was reduced to 200…

Let the actual time taken be x hours.

Original speed = 600 / x km/h. After the problem the journey takes 30 minutes (0.5 hour) more, so the new time is x + 0.5 hours and the new speed = 600 / (x + 0.5) km/h.

We are told the speed is reduced by 200 km/h, so

600 / x - 600 / (x + 0.5) = 200

Multiply both sides by x(x + 0.5):

600(x + 0.5) - 600x = 200 x (x + 0.5)

Simplify the left side: 600x + 300 - 600x = 300, so

300 = 200x^2 + 100x

Divide both sides by 100: 3 = 2x^2 + x, or 2x^2 + x - 3 = 0.

Solve the quadratic: x = [ -1 ± sqrt(1 + 24 ) ] / 4 = [ -1 ± 5 ] / 4.

The positive root is x = ( -1 + 5 ) / 4 = 1 hour.

Therefore the actual time taken for the journey is 1 hour.