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

Let us assume the total time be n minutes

We know that,

Distance covered = = Speed × Time

∴Total distance covered by thief in n minutes = (50 × n) m

= 50n m

Also, Total distance covered by policeman = 1^st min. + 2^nd min. + …… (n – 2) terms

Here, we have

a = 60, d = 5 and ‘n’ = n - 2

_{We know that,}

100n = (n – 2) [120 + 5n – 15]

5n² + 105n – 10n – 210 – 100n = 0

5 (n² – n – 42) = 0

_n² – 7n + 6n – 42 = 0

_{(n – 7) (n + 6) = 0}

_{∴ n = 7 or n = - 6 [Not possible as time cannot be negative]}

_{Hence, Time taken by the policemen to catch the thief = (n – 2)}

_{= (7 – 2) = 5 minutes}