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Question:A thief runs with a uniform speed of 100 m/minute.After one minute a policeman runs after the thief tocatch him. He goes with a speed of 100 m/minute in thefirst minute and increases his speed by 10 m/minuteevery succeeding minute. After how many minutes thepoliceman will catch the thief. |
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Answer» Let the police catch the thief in n min As the thief ran 1 min before the police...time taken by the thief before being caught = (n+1) min Distance travelled by the thief in (n+1) min = 100(n+1)m Speed of police in 1st min=100m/min Speed of police in 2nd min=110m/min ...3rd min = 120m/min.........so on 100,110,120,............ this forms an AP Total distance travelled by the police in n min = n/2(2 x 100 +(n-1)10) On catching the thief by police,distance traveled by thief= distance travelled by the police 100(n+1)= n/2(2 x 100 + (n-1)10) 100n + 100= 100n +n/2(n-1)10 100=n(n-1)5 n2-n-20 = 0 (n-5)(n+4) = 0 n-5 = 0 n= 5 OR n= -4...(but this is not possible) so, n= 5 Time taken by the policeman to catch the thief = 5min |
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