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A thief away from a police station with a uniform speed 100m/min. After 1 min a policeman runs behind the thief to catch him. He goes at a speed of 100m/min in 1st min and increases the speed 10m/min on each succeeding min. After how many minutes the policeman catches the thief.
Asked by Kumarashish6345 | 21 Feb, 2019, 06:22: AM
Let after n minutes, thief was caught by police.

Distance travelled by police every one minute duration from beginning = 100+110+120........+[ 100+(n-1)10 ]

Above series of distances is in Arithmetic progression.

Sum of the distances of above Arithmetic progression is same as the distance travelled by thief

(n/2)[ 200+ (n-1)10 ] = (n+1)×100

above expression is simplified as,  n2 -n -20 =0   or   (n-5)(n+4) = 0

hence n=5 is the feasible solution.  Thief is caught by police after 6 min
Answered by Thiyagarajan K | 21 Feb, 2019, 07:56: AM

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