Latest CAT Aptitude Question SOLUTION: Two stations A and B are 660 km apart. A train T1, which stops for 7 minutes at every town-station and for 3 minutes at every village-station, started from A with a speed of 40 km/

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Two stations A and B are 660 km apart. A train T1, which stops for 7 minutes at every town-station and for 3 minutes at every
village-station, started from A with a speed of 40 km/hr towards B and at the same time a train T2 with a speed of 60 km/hr, which
does not stop at any intermediate station, started from B towards A. They cross each other at C which is 420 km away from B. If the
number of town-stations between A and C is less than the number of village-stations, then at least how many stations - town or
village - are there between A and C? Assume that T1 stops only at town or village-stations.
(1) 10
(2) 16
(3) 20
(4) 13

Asked In CAT (10 years ago)

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P.Someshwar Reddy  (10 years ago)

Option 2: 16 stations

Given Distance between A and B is 660km.

Train T1 and Train T2 cross each other at C which is 420km from B,
so distance of it from A is 240km(660-420=240).

Time taken by Train T2 to reach C is
420km/60kmph = 7hr
(Given Speed of Train T2 is 60kmph)

In 7hr Train T1 can reach 280km(Given speed of Train T1 is 40kmph),
but it is able to reach 240km only.
With 40km/hr Train T1 can reach in 6hr a distance of 240km, but they crossed each other at 7hr so there is a elapse of 1hr(60mins).

Given Train T1 stops for 7minutes at every town-station and 3 minutes for every village-station and also given number of town-stations between A and C is less than the number of Village-stations(towns < village).

So let number of town-stations be X
number of Village-stations be Y
i.e. 7X+3Y=60(because time elapsed is 60mins)

Giving Vales to X and Y it will be found that X=3 and Y=13.
So the total number of stations are X+Y= 16stations

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