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ICSE Class 10 Answered

A thief after commiting theft runs at a uniform speed of 50m/min. After 2min à policeman runs to catch him . He runs 60 m in the first minute and increases his speed by 5 m/ min every success given min . After how many mind the policeman will catch the thief ?  
Asked by Anmolrishiket | 30 Jan, 2019, 12:35: PM
answered-by-expert Expert Answer
Policeman runs a distance in first minute = 60m
for every successive minute, his running ditance increases by 5m.
 
if he catches thief after n minutes, then total running distance of police = 60+65+70+......[60+(n-1)5]  ...............(1)
 
Series given in (1) is arithmetic progression with first term 60 and common difference 5
 
Total distance covered by police in n minutes = (n/2) [ 2×60 + (n-1)5 ]  .......................(2)
The distance given by eqn.(2) is same as the distance covered by thief in (n+2) minutes with running speed 50m/min
 
hence we have,  (n/2) [ 2×60 + (n-1)5 ] = 50×(n+2)  ...........................(3)
 
Eqn.(3) can be simplified as ,  n2 + 3n -40 = 0  .................(4)
by factorising LHS of eqn.(4), we have,  (n+8)(n-5) = 0 ............................(5)
 
hence n = 5,  police will catch thief after 5 minutes from his starting time.
Answered by Thiyagarajan K | 30 Jan, 2019, 03:43: PM
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