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24. A thief away from a Police Station with a uniform speed 100m/minutes. After one minutea Policeman runs behind the thief to catch him. He goes at a speed of 100m/minute in firstminute and tncreases the speed 10m/minute on each succeeding mimute. After how manyminutes the Policeman catches the thiet.Now answer these questions:) Which mathematical concept is being used to solve the above problem?() Which trait of personality of the policeman is showed? |
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Answer» Let the policeman catch the thief in n minutes. Given that uniform speed of the thief = 100m/min. Given that After 1 minute a policeman runs to catch him at the speed of 100 in first minutes. (n + 1) minutes = 100(n + 1) minutes. Given that speed of policeman increase by 10m/min. The speed of police in 1 minute = 100m/min. The speed of police in 2 minutes = 110m/min. The speed of police in 3 minutes = 120m/min. The speed of police in 4 minutes = 130m/min. Hence 100,110,120,130 are in AP. Let a be the first term and d be the common difference. a = 100,d = 110 - 100 = 10. We know that sum of n terms of an ap = n/2(2a + (n - 1) * d) = n/2(2(100) + (n - 1) * 10) ------ (1) The distance traveled by the thief = Distance traveled by the police 100(n + 1) = n/2(2 * 100+ (n - 1) * 10) 100n + 100 = n/2(200 + 10n - 10) 200n + 200 = 10n^2 + 190n 10n^2 + 190n - 200 = 200n 10n^2 - 10n - 200 = 0 n^2 - n - 20 = 0 n^2 -5n + 4n - 20 = 0 n(n - 5) + 4(n - 5) = 0 (n -5)(n + 4) = 0 n = 5 (or) n = -4. n cannot be negative. Therefore the time is taken by the policeman to catch the thief = 5minutes. |
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