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In 900 metres long tunnel has two ends X and Y.  A Thief is 100 metres away from the end X when he see a police Jeep approaching from the side.   he calculate that irrespective of the direction he runs in he run in he would be caught exactly at one of the end of the tunnel. what is the ratio of speed of the thief and the police jeep?

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2 people found it helpful

Answer: 7:9

Step-by-step explanation:

Let distance of police from End X = A

Speed of Thief = T

Speed of Police = P

Case 1: If thief runs toward End Y.

Time=Distance/Speed

Time(thief)=800/T  

Time(police)=(A+900)/P

Both time should be equal as thief gets caught in end

800/T = (A+900)/P

T/P = 800/(A+900)

Case 2: If thief runs towards End X

Time(thief) = 100/T

Time(police) = A/P

Both time should be again equal

100/T=A/P

T/P=100/A

Both the ratios of T/P should be equal, so it becomes

800/(A+900) = 100/A

Cross multiply

100(A+900) = 800A

100A + 90000= 800A

700A=90000

A= 900/7

Put this value of A in T/P ratio of Case 2(You can put in case 1 also)

T/P=100/(900/7)

T/P= 100*7/900

T/P=7/9

T:P=7:9

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