SEP01 – Problems on Trains

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    Today, We are going to take a test on Problems based on Train.

    Before you take the test read these posts to be comfortable.

    Shortcuts and Tips for Train Problems                                                

    Important Formulae

    1, km/hr to m/s conversion:

        a km/hr =\left(a\;x\frac5{18}\right)m/s.

    2, m/s to km/hr conversion:

    a m/s =\left(a\;x\frac{18}5\right)km/hr.

    3,  Formulas for finding Speed, Time and Distance

              (i)  Speed, Time and Distance:

                  Speed =\left(\frac{Dis\tan ce}{time}\right) , Time = \left(\frac{Dis\tan ce}{speed}\right) , Distance = (Speed x Time).

             (ii) km/hr to m/sec conversion:

                    x km/hr =\left(x\;x\frac5{18}\right)m/sec.

             (iii) m/sec to km/hr conversion:

                   x m/sec =\left(x\;x\frac{18}5\right)km/hr.

             (iv) If the ratio of the speeds of A and B is a : b, then the ratio of the the times taken by then to cover the same distance is \frac1a:\frac1bor b : a.

               (v) Suppose a man covers a certain distance at x km/hr and an equal distance at y km/hr. Then,the average speed during the whole journey is \left(\frac{2xy}{x+y}\right)km/hr.

    4,  Time taken by a train of length l metres to pass a pole or standing man or a signal post is equal to the time taken by the train to cover l metres.

    5, Time taken by a train of length l metres to pass a stationery object of length b metres is the time taken by the train to cover (l + b) metres.

    6, Suppose two trains or two objects bodies are moving in the same direction at u m/s and v m/s, where u > v, then their relative speed is = (uv) m/s.

    7, Suppose two trains or two objects bodies are moving in opposite directions at u m/s and v m/s, then their relative speed is = (u + v) m/s.

    8, If two trains of length a metres and b metres are moving in opposite directions at u m/s and v m/s, then:

    The time taken by the trains to cross each other = \left(\frac{a+b}{u+v}\right)sec.

    9, If two trains of length a metres and b metres are moving in the same direction at u m/s and v m/s, then:

    The time taken by the faster train to cross the slower train =\left(\frac{a+b}{u-v}\right)sec.

    10, If two trains (or bodies) start at the same time from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then:

    (A’s speed) : (B’s speed) = \left(\sqrt b:\sqrt a\right).

     

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