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A police saw a Thief at a distance of 2km. When Police started chasing him Thief also started running. If the ratio of Speeds of Police to Thief is 5:4. Then thief was caught at a certain distance then how many Kms did police run to catch the Thief?
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A police saw a Thief at a distance of 2km. When Police started chasing...
Problem Statement:

A police saw a Thief at a distance of 2km. When Police started chasing him Thief also started running. If the ratio of Speeds of Police to Thief is 5:4. Then thief was caught at a certain distance then how many Kms did police run to catch the Thief?


Solution:


Step 1: Identify the Given Parameters


  • Distance between Police and Thief = 2km

  • Ratio of Speeds of Police to Thief = 5:4



Step 2: Calculate the Speeds of Police and Thief


  • Let the speed of Police be 5x kmph

  • Let the speed of Thief be 4x kmph



Step 3: Calculate the Time taken by Police and Thief


  • Let the time taken by Police to catch the Thief be t hours

  • Then, the time taken by Thief to run away from Police is also t hours



Step 4: Calculate the Distance covered by Police and Thief


  • Distance covered by Police = Speed * Time = 5x * t

  • Distance covered by Thief = Speed * Time = 4x * t



Step 5: Calculate the Total Distance covered by Thief


  • Total Distance covered by Thief = Distance between Police and Thief + Distance covered by Thief before being caught = 2 + 4x * t



Step 6: Equate the Total Distance covered by Thief to the Distance covered by Police and Solve for t


  • 2 + 4x * t = 5x * t

  • 3x * t = 2

  • t = 2/(3x)



Step 7: Calculate the Distance covered by Police to Catch the Thief


  • Distance covered by Police = Speed * Time = 5x * t = 5x * (2/(3x)) = 10/3 km



Answer:

The Police had to run 10/3 km to catch the Thief.
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A police saw a Thief at a distance of 2km. When Police started chasing him Thief also started running. If the ratio of Speeds of Police to Thief is 5:4. Then thief was caught at a certain distance then how many Kms did police run to catch the Thief?
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