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CAT 1999 | Question: 72

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Navjivan Express from Ahmedabad to Chennai leaves Ahmedabad at 6.30 a.m. and travels at 50 kmph towards Baroda situated 100 km away. At 7.00 a.m. Howrah-Ahmedabad Express leaves Baroda towards Ahmedabad and travels at 40 kmph. At 7.30 a.m. Mr Shah, the traffic controller at Baroda realizes that both the trains are running on the same track. How much time does he have to avert a head-on collision between the two trains?

  1. 15 min
  2. 20 min
  3. 25 min
  4. 30 min

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ahmedabad .........100 km...........baroda

(navjeevan express )   ........                      (howrah- ahmedabad)

 leaves at 6.30 am from ahmedabad      .......         leaves at 7.00 am from baroda

speed=50 kmph                            ......                            speed=40 kmph

now bcz traffic controller realize  about problem at 7.30...firstly i have to find distance travelled by both train till 7.30

distance travelled by navjeevan express till 7.30=1h*50=50km

distance travelled by howrah ahmedabad till 7.30=1/2h*40=20 km

now we can see both trains moving towards each other so 

remaining distance=100km-(50+20) km=30 km

relative speed=(50+40)kmph =90 kmph

so time remaining to avert head on collision=30km/90kmph=1/3 h=20 min                                                               

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