A thief after committing a theft runs at a uniform speed of 50 m/min. After 2 min a policeman runs to catch him .He goes 60 m in first min. and increases his speed by 5m/min every succeeding minute. After how many min. the policeman will catch the thief??
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1
answer of this question is 7 min.
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Answer:
According to the question,
Distance between thief and police after 2 minutes = 100 m
Police starts chasing thief with initial speed of 60 and increasing his speed by 5 m every minute.
Let the police chase the thief for t minutes.
Implies, thief covers total 100 + 50t m
Police runs with following pattern 60,65,70...
This is an Arithmetic Progression with a = 60, d = 5 & number of terms = t
t/2(2×60+(t−1)×5)=50t+100
t×(120+5t−5)=100t+200
5t
2
+15t−200=0
t
2
+3t−40=0
t={−3±
(9+160)}/2
=(−3±13)/2=+5
Implies, police will catch thief in 5 minutes
or the thief will be caught in 7 minutes
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