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A thief is spotted by a policeman from a distance of 100 metres. when the policeman starts the chase, the thief also starts running. If the spped of the thief be 8km/hr and that of policeman 10km/hr, how far the thief will have run before he is overtaken?

A thief is spotted by a policeman from a distance of  100 metres. when the  policeman starts the chase, the thief also starts running. If the spped of the thief be 8km/hr and that of policeman 10km/hr, how far the thief will have run before he is overtaken?

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5 Answers

Hanumant Gusain
39 Points
9 years ago

their time will same so by equating

distanceby theif/speed of theif = distance by police/speed of police

(.1+x)/8 = x/10

by simplifying x = .5 km

hence theif will move .1+.5=.6 km = 600mt

rishabh
27 Points
9 years ago

400m .4km

let after time t the policeman will oertake thief and the distance from the current position of thief be x km

then at time when policeman will overtake the thief the time taken by the policeman to run (x+.1)km = xkm covered by thief thus on equating the time expression for both policeman and thief we get the required answer

 

 

 

 

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Rohit Suri
37 Points
9 years ago

Let us assume that the time taken by the policeman to catch the thief is t hrs.

Hence, after time t, the thief will be at a distance of t*8 km from where he started. At the same time he will be at a distance of (t*8) + 0.1 km from where the police started.

As the police catches the thiefr in time t, he will have to run a distance of (t*8) + 0.1 km.

Now, distance run by police in time t= 10*t km.

Therefore, 10t = 8t + 0.1 => 2t= 0.1 => t=0.05 hrs

Distance run by thief in 0.05 hrs = 8*0.05 = 0.4km = 400m

 

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saurabh negi
16 Points
9 years ago

Let p=policeman,  t =theif
Veocity:v(p)= 10km/hr=10.5/18 m/sec=25/9 m/sec
Similarly, v(t)=20/9 m/sec
As the velocity is uniform, we can use the formula,dist=v.t
Let policeman overtakes the theif at a dist. d from the theif, so 
the time taken to meet at that point will be same for both of them.
i.e. t(p)=t (t)
Therefore, (100+d)/v (p)=d/v(t)         ( time= dist/v  and policeman has to cover 100m more than theif)
 by putting the values  of velocities and solving we get d=400 m.

TANAYRAJ SINGH CHOUHAN
65 Points
9 years ago
Let us assume that the thief travels `x` meters before he is caught by the policeman. So, the policeman travels a distance of `x+100` meters. In travelling this distance bot the thief and policeman require equal time so by equating time take by both we can get the solution to the problem. So, Time taken by thief = x/8 " " " policeman = x+100/10 Equating both times, x+0.100/10 = x/8 x = 0.400km = 400 m PLEASE APPROVE MY ANSWER IF YOU ARE SATISFIED BY IT. AND BEST OF LUCK FOR YOUR PREPARATION.

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