There is a regular bus service between Pune and Mumbai (180km apart) at every ho

Question

There is a regular bus service between Pune and Mumbai (180km apart) at every
hour from both the ends, from 4am to 11pm. These busses run at average speed
of 45km/hr. Taxies also run on the same route at 60km/hr with regular interval of
30min from 5am to 10pm. Following statements are based upon the number of taxies
or busses crossed (not overtaken) only during travelling i.e. excluding instances of
arrival and departure. Select the correct statement(s).
(a) First bus crosses 6 taxis.
(b) Last taxi crosses 5 buses.
(c) Bus left at 8pm crosses 10 taxis.
(d) Taxi left at 12 noon crosses 6 buses.

Explanation / Answer

Ans = (a), (b), (c) and (d) Bus covers the distance in 4 hours, taxi in 3 hours. First ST bus is at 4am and it will reach its destination at 8am. Thus, during the journey, it will meet all taxis to have started from the other city from 5 am till 7:30 am. i.e. 5:00, 5:30, 6:00, 6:30, 7:00, 7:30 = 6 taxis Last taxi starts at 10:00 pm, by which 6:00 pm bus would have arrived at the bus station. It reaches well past 11:00 pm (time of last bus). Thus, it will meet all the buses after the 6:00 pm bus. i.e. 7:00, 8:00, 9:00, 10:00, 11:00 = 5 busses. The taxi leaving at 5:00 pm would have arrived by 8:00 pm. Thus bus will meet all taxis from 5:30 pm till the last taxi which leaves at 10:00pm i.e. 5:30, 6:00, 6:30, 7:00, 7:30, 8:00, 8:30, 9:00, 9:30, 10:00= 10 taxis The 8:00 am bus would have arrived by noon. Thus the taxi meets 9:00am, 10:00am, 11:00am, 12:00noon, 1:00pm, 2:00pm buses on the way = 6 buses

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