A thief seeing a policeman at a distance of 150 metres starts running at 10 kmph and the policeman gives immediate chase at 12 kmph. When the thief is overtaken the thief has traveled a distance of:

Explanation:-

P__150m___T______X m (Let)_______Q.
Let Policeman caught thief at a distance (X + 150)m. And Thief has traveled X m.
Speed of Policeman = 12 kmph = ^(12*5)/₁₈ = ⁶⁰/₁₈ m/sec.
Speed of thief = 10 km = ^(10*5)/₁₈ = ⁵⁰/₁₈ m/sec.
In this case time is constant means Policeman covered (X + 150)m in same time thief covered X m.
Thus,
Speed of the thief /Speed of Policeman = ^X/_(150+X)
⁵⁰/₆₀ = ^X/_(150+X)
7500 + 50X = 60X
10X = 7500
X = 750 m.
So, Thief has traveled 750 m before the caught.