Q. 314.6( 14 Votes )

A thief, after co

Answer :

Let us assume the total time be n minutes

We know that,


Distance covered = = Speed × Time


Total distance covered by thief in n minutes = (50 × n) m


= 50n m


Also, Total distance covered by policeman = 1st min. + 2nd min. + …… (n – 2) terms


Here, we have


a = 60, d = 5 and ‘n’ = n - 2


We know that,




100n = (n – 2) [120 + 5n – 15]


5n2 + 105n – 10n – 210 – 100n = 0


5 (n2 – n – 42) = 0


n2 – 7n + 6n – 42 = 0


(n – 7) (n + 6) = 0


n = 7 or n = - 6 [Not possible as time cannot be negative]


Hence, time taken by the policemen to catch the thief = (n – 2)


= (7 – 2) = 5 minutes

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