[CAT 1990] A car after travelling 18 km from a point A developed some problem in the engine and speed became (4/5)^th of its original speed. As a result, the car reached point B 45 minutes late. If the engine had developed the same problem after travelling 30 km from A, then it would have reached B only 36 minutes late. The original speed of the car (in km per hour) and the distance between the points A and B (in km) is

Let the original speed be v km/h and the total distance be D km. The late time difference between the two scenarios occurs only over the 12 km stretch from 18 km to 30 km, where the car travels at its original speed in one case and at (4/5)v in the other, giving the equation 12/(4v/5) - 12/v = 9/60. Solving this yields an original speed of 10 km/h, and using the first scenario to find the total distance gives (D - 18)/(4/5 times 10) - (D - 18)/10 = 45/60, which results in D = 48 km. Since 10 km/h and 48 km do not match any of the listed pairs, the correct choice is None of these.

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