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A thief after committing a theft, …

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A thief after committing a theft, runs at a uniform speed of 50m/min. After 2 minutes, a policeman runs to catchbhim. He goes 60 m in 1st min and increases his speed by 5m/min every succeding min. After how many minutes, the policeman will catch the thief?

Posted by ☆ Pranal Rewatkar ☆ 6 years, 10 months ago

CBSE > Class 10 > Mathematics

1 answers

Sithara Parwin 6 years, 10 months ago

Thief has a lead of 50*2 = 100m Relative distance covered by cop in 1st min = 60-50 = 10 Relative distance covered by cop in 2nd min = 65-50 = 15 Relative distance covered by cop in 3rd min = 70 -50 = 20 10, 15, 20 ... is an AP whose sum is 100 a= 10 , d = 5 Sum = 100 100 = n/2(2a + (n-1)d) = n/2(20 +(n-1)5 ) 100= n/2(20 + 5n -5) 200 = n(15 + 5n) divide by 5 40 = n(n + 3) n^2 + 8n - 5n - 40 =0 n(n+8) - 5(n+8)= 0 >> n = 5 as it cant be negative Therefore cop catches after 5 min + 2min (when cop was at rest) = 7min

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