A train 360m in length, travelling at a uniform speed overtake a car,travelling parallel to the tracks at 72 kmph and passed it in 12 sec. Fortyeight minutes later,the train starts overtaking a cyclist and passed him in 9 sec.How much time after the train overtook the cyclist would the car over take him?

- 2hrs 24min 36 sec
- 3hrs 49min 49 sec
- 3hrs 12min 9 sec
- 2hrs 24min 27 sec

Here, speed of car is 72kmph.

we will convert it to meter per second

72kmph = (72 * 5)/18 = 20mps

First we will find speed of Train, Car(given) and cycle.

Scar = 20 m/s

S_{train} = x m/s

S_{cycle} = y m/s

Train overtake the car in 12 seconds.

Both are travelling in same direction.

Speed * Time = Distance

Relative Speed of Train will be (x - 20)

therefore (x -20)12 = 360

On solving x = 50m/s

Now Train overtake Cycle in 9 second

Relative speed will be (50-y)

therefore (50-y)9 = 360

On solving y = 10m/s

We got speed of all three vehicles.

Scar = 20 m/s

S_{train} = 50 m/s

S_{cycle} = 10 m/s

Now we will find time taken by car to overtake cycle.

Let us assume that all this start at 12:00

At 12:48 Distance between Car and Train =30*48*60 =86400 meters.

At this time Train and cycle will be at same place

Question says that after overtaking car, Train started overtaking cycle

which means before 48 min train has just passed car and distance between car and twain was 360meter(aslength of train is 360)

Therefore distance between cycle and Car at 12:48:00 will be 86400 + 360 = 86760 meters.

Now after 9 seconds cycle will cover 90 meter and car will cover 180 meter.

relative distance = 86760 - 90 = 86670 meter

relative speed = 20-10 = 10m/s

Time = 86670/10 = 8667 seconds

which is equivalent to 2 hr 24 min 27 sec

Hence option D