infy puzzle

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.
also
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.?
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Commented:
is the distance between police and thief 27 theif steps, or 27 officer steps?
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Billing EngineerCommented:

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

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

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Billing EngineerCommented:
good spot, ozo !!
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Commented:
If the distance is 27 theif steps, then it will take the officer 30 steps to catch the theif
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Commented:
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.
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