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    From a taxi stand, two cabs start at a speed of 54 km/hr at an interval of 29 minutes, both cabs travelling in the same direction. A man coming i
    Question

    From a taxi stand, two cabs start at a speed of 54 km/hr at an interval of 29 minutes, both cabs travelling in the same direction. A man coming in the opposite direction towards the taxi stand meets the cabs at an interval of 12 minutes. Find the speed (in km/hr) of the man.​

    A.

    74.8

    B.

    82.1

    C.

    76.5

    D.

    80.4

    Correct option is C

    Given:

    Speed of each cab vc=v_c =​ 54 km/h.

    Start interval between cabs = 29 min.

    The man, moving in the opposite direction, meets the two cabs at an interval of 12 min.

    Formula Used:

    Separation between cabs (same speed) d = vc×start intervalv_c \times \text{start interval}​​

    Relative speed (cab vs man, opposite directions) = vc+vm.v_c + v_m.​​

    Time between successive meetings =dvc+vm=\dfrac{d}{v_c+v_m}​​

    Solution:
    Convert minutes to hours where needed.
    d = 54×2960=26.1 km54 \times \frac{29}{60} = 26.1\ \text{km}​​
    Given the man meets them 12 min apart = 1260=\frac{12}{60}=​0.2 h,

    0.2 =26.154+vm= \frac{26.1}{54 + v_m}

    54+vm=26.10.2=130.54 + v_m = \frac{26.1}{0.2} = 130.5​​

    vm=130v_m = 130​.5 - 54 = 76.5 km/h

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