infy puzzle

Posted on 2006-04-11
Last Modified: 2008-02-26
the distance between police and thief is 27 steps when the police officer starts running after him.the time reqired by thief 2 take 8 steps=time required by officer 2 take 5 steps.
distance travelled by thief in 5 steps =distance travelled by officer in 2 steps.
how many steps the officer needed to catch up with the thief.?
Question by:shilpi84
    LVL 84

    Expert Comment

    is the distance between police and thief 27 theif steps, or 27 officer steps?
    LVL 142

    Expert Comment

    by:Guy Hengel [angelIII / a3]

    distance X = 1 unit
    thief: 1 step = 1/5 units
    officer: 1 step = 1/2 units

    time T = 1 unit
    thief: 8 steps/unit : 1 step = 1/8 units  
    officer: 5 steps/unit : 1 step = 1/5 units

    thief: 8 * 1/5 = 8/5 = 1,6  d/t
    officer: 5 * 1/2 = 5/2 = 2,5  d/t

    speed difference:
    officer will gain 0.9 distance units / time unit
    0.9 distance units = 1,8 officer steps / time unit
    hence 27/1,8 = 45 time units for the officer to get the thief

    LVL 142

    Expert Comment

    by:Guy Hengel [angelIII / a3]
    good spot, ozo !!
    LVL 84

    Assisted Solution

    If the distance is 27 theif steps, then it will take the officer 30 steps to catch the theif
    LVL 9

    Accepted Solution

    I assume that the distance is 27 officer steps.

    The officer's step takes t time and during that time he advances s.
    The thief's step takes 5/8*t time and during that time he advances 2/5*s.
    While the officer takes 1 step, the thief can take 8/5 steps, so he advances 8/5*2/5*s = 16/25*s
    For each step of the officer the distance decreases by (1-16/25)*s = 9/25*s

    So the distance can be taken by the officer by 27/(9/25) = 75 officer steps.
    LVL 5

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