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Question

After travelling for 30 minutes a train meets with an accident, due to which it has to stop for 45 minutes. Due to the accident its speed is also reduced to 23 of its former value and the train reaches its destination 1 hour 30 minutes late. Had the accident occurred 60 km later, the train would have reached 30 minutes earlier. The length of journey is

A
90 km
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B
120 km
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C
150 km
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D
180 km
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Solution

The correct option is B 120 km
Let d be the distance from point of first accident to destination and s be the speed of train.
1stcase
ds+34=d2s3 (34hr=45minutes)
ds+34=32ds Time=DistanceSpeed
34×ds(321)=12sds=t=32hr
Train got late by 1hr30min(90min)
Actual delay due to speed resolution =(9045)min=45min

2ndcase
30minutes could have been saved because of train travelling 60km more with speed s
Time difference if it would have travelled this 60km with 253 speed is nothing but due to same 30minutes(12hr)
60s+606s3=1260s+90s=1230s=12s=60km/hr
Initially train travelled for 30min
Distance travelled before accident =602km=30km
After accident the train travel dkm
ds=32d=32×s=32×60km=90km
Total length of journey =30km+90km=120km

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