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Answers
Let suppose thief take n min when it got caught by police whereas police would take (n-1) min to catch the thief as police starts running after 1min
Distance covered by thief= speed×time= 100×n=100n
As you can see in case of police it is in the form of AP, so the distance covered by police=Sn-1=
(n-1)/2[2×100+(n-2)×10]
As we know,
Distance covered by police=Distance covered by theif
in order to catch the thief
(n-1)/2[200+(n-2)×10]=100n
10(n-1)/2[20+(n-2)]=100n
(n-1)/2[20+n-2]=10n
(n-1)[n+18]=20n
n^2+18n-n-18=20n
n^2+17n-18=20n
n^2-3n-18=0
n^2-6n+3n-18=0
n(n-6)+3(n-6)=0
(n+3)(n-6)=0
n= -3 cannot be possible as time cannot be negative
OR
n=6 hence thief's time of caught is 6min
Now police time = n-1= 6-1=5min
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