A thief runs from a police station at a uniform speed of 100m per.after 1 minute a policeman runs behind the thief to catch him.he goes at a speed of 8m/minute in the first minute and increases his speed by 10m/minute in each succeeding minute.after how many minutes will the policeman catch the thief



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Let us suppose after t min policeman will catch the thief.
Then the distance travelled by policeman and thief will be same.
distance travelled by thief = 100t
now, for policeman,
distance = 8+ 18 +28 +38 +..... to t terms
sum= (t/2)(2×8 +(t -1)10)
(t/2)(2×8 +(t -1)10) = 100t
⇒16 +(t -1)10 =200
⇒10t -10 =184
⇒10t =194
t = 19.4min
or time = 19min 24sec