A thief pursued by a policeman was 150 m ahead at the start. If the ratio of the speed of the policeman to that of the thief was 5 : 4, then how far (distance in metres) could the thief go before he is caught by the policeman?

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Let the speed of the policeman be 5x and the speed of the thief be 4x.

The initial lead of the thief is 150 m.

The relative speed of the policeman with respect to the thief = (5x - 4x) = x.

Time taken by the policeman to catch the thief = Distance / Relative speed = 150 / x.

Distance covered by the thief in this time = speed of thief × time = 4x × (150 / x) = 600 m.

Therefore, the thief can run 600 meters before being caught.

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