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  • apptitude train problem

    naga lakshmi

    Member

    Updated: Oct 26, 2024
    Views: 1.5K
    1.At 8 p.m., Vaigai Express from Madurai and The Chennai Express from Chennai are moving in opposite direction at 40 km/hr and 60 km/hr. At Trichy, they meet each other. If the distance covered by the Chennai Express was 100 km more than the Vaigai Express at Trichy, then the distance between Chennai and Madurai is?
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  • simplycoder

    Member • Jan 13, 2012

    naga lakshmi
    1.At 8 p.m., Vaigai Express from Madurai and The Chennai Express from Chennai are moving in opposite direction at 40 km/hr and 60 km/hr. At Trichy, they meet each other. If the distance covered by the Chennai Express was 100 km more than the Vaigai Express at Trichy, then the distance between Chennai and Madurai is?
    For all those guys who are unaware of madhurai,chennai,tirchy, its like this:
    Chennai-----Tirchy-----Madhurai.

    So assume the distance travelled by Vaigai express is x.km and Chennai express is y.km
    also the time required by both trains is t units.

    By fundamental formula, Distance=Speed*Time.

    x=40*t.....(1)
    y=60*t.....(2)

    By problem statement, y=x+100.
    so x+100=60*t......(3)
    divide (1) by (3)
    So that gives us the distance between Madhurai and Tirchy to be 200km and Tirchy and Chennai to be 300km.

    So the distance between Madhurai and Chennai is 200+300=500km
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  • naga lakshmi

    Member • Jan 13, 2012

    It's right answer😀
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  • naga lakshmi

    Member • Jan 14, 2012

    2. A train A leaves from Agra at 4.30 a.m. and reaches Delhi at 7.30 a.m. And a train B leaves from Delhi at 6.30 a.m. and reaches Agra at 8.30 a.m. At what time do the two trains cross each other?👍
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  • Sagar07

    Member • Jan 14, 2012

    naga lakshmi
    2. A train A leaves from Agra at 4.30 a.m. and reaches Delhi at 7.30 a.m. And a train B leaves from Delhi at 6.30 a.m. and reaches Agra at 8.30 a.m. At what time do the two trains cross each other?👍
    Two trains will cross each other at 6.54 a.m....
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  • naga lakshmi

    Member • Jan 14, 2012

    Sagar07
    Two trains will cross each other at 6.54 a.m....
    Yes, It's absolutely correct😁
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  • simplycoder

    Member • Jan 15, 2012

    naga lakshmi
    Yes, It's absolutely correct😁
    I have seen this question in some placement paper before, don't remember which.

    Anyways, a typical explanation might be some thing like this.

    Let the speed of the train A be Sa and that of B be Sb. Now from the data, we know that train A reaches the destination in 3hrs. and train B reaches in 2hrs. Since they cover the same amount of distance, let us assume the distance from Agra to Delhi is d.km. From time, we can say that Sa=(d/3)kmph and Sb=(d/2) kmph.

    Since both the trains would approach each other and move in opposite direction, it can be said that the relative velocity is Sa+Sb.

    Now From the timings, we know that they will meet each other before 7:30 am and after 6:30 am.
    We also know that train A starts the journey 2 hrs before train B. So even before B starts, A will cover some part of the distance d.

    So let us keep train A as reference. Due to this we can say that if train A is running for Ta hrs, then train B will run in (Ta-2) hrs.

    By simple concept of distance and relative velocity, we can form equation like this.
    (d/3)*Ta+(d/2)*Tb=d.
    so (d/3)*Ta+(d/2)*(Ta-2)=d
    Cancel d through-out and by simplification, Ta=12/5 hrs = 2hrs 24 mins.
    So after completing 2hrs and 24 mins, Train A will meet train B.

    So the time is 6:54 am.(4:30am+12/5 hrs) and this answer satisfies the condition that they meet before 7:30am and after 6:30am.
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  • Dancer_Engineer

    Member • Jan 15, 2012

    @SC, very good explanation. 👍
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  • naga lakshmi

    Member • Jan 15, 2012

    ok i give u another way of solution

    Solution :
    Let the distance between Delhi and Agra be X.
    And let the train A meet the train B be Y hours after 6.30 a.m.
    Then, train A covers X km in 3hrs and B covers X km in 2hrs. (you can find the durations of travel from the time of start and arrivals of the trains as given in question)
    Therefore, Speed of Train A = X / 3 km/hr and Speed of Train B = X / 2 km/hr
    Distance covered by the train A in (Y+2) hrs + Distance covered by the train B in Y hrs = X. (We are using Y + 2 hours in this equation for train A as it has started 2 hours earlier)
    (X/3) x (Y+2) + (X/2) x Y = X
    Y/3 + 2/3 + Y/2 = 1
    5Y = 2
    Y = 2/5 hr.
    Y = (2/5) x 60 min = 24 min.
    Hence, the train A meet the train B at 6.54 a.m.
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