Motor-cyclist P started his journey at a speed of 30 km/hr. After 30 minutes, motor cyclist Q started from the same place but with a speed of 40 km/hr. How much time will Q take to overtake P?
[A]$1\ hours$
[B]$\frac{3}{8}\ hours$
[C]$\frac{3}{2}\ hours$
[D]$2\ hours$

$\mathbf{\frac{3}{2}\ hours}$
Distance covered by motor cyclist P in 30 minutes.
$= 30\times \frac{1}{2} = 15\ km$
Relative Speed = 40 – 30 = 10 km/hr
∴ Required Speed = Time taken to cover is km at 10 km/hr
$= \frac{15}{10} = \frac{3}{2}\ hours$
Hence option [C] is correct answer.