A police station, a bank and a safe house for the thief are in a straight line with a bank in between. The distance between the police station and the safe house is four times the distance between the bank and the safe house. After looting the bank at 9:15 A.M, the thief runs away. A policeman gets the information instantly and chases him at the speed of 16 km/h. The policeman catches the thief at the gate of the safe house in fifteen minutes. What is the distance between the bank and the police station?

A police station, a bank, and a safe house for the thief are in a straight line with the bank in between. The distance between the police station and the safe house is four times the distance between the bank and the safe house. After looting the bank at 9:15 A.M, the thief runs away. A policeman gets the information instantly and chases him at the speed of 16 km/h. The policeman catches the thief at the gate of the safe house in fifteen minutes.

Formula used:

Speed = Distance / Time

Calculation:

Time taken by the policeman = 15 minutes = 15/60 hours = 1/4 hours

Speed of the policeman = 16 km/h

Distance covered by the policeman in 1/4 hours:

⇒ Distance = Speed × Time

⇒ Distance = 16 × 1/4

⇒ Distance = 4 km

Let the distance between the bank and the safe house be x km.

Then, the distance between the police station and the safe house = 4x km.

Given, the bank is in between the police station and the safe house:

⇒ Distance between police station and bank = 4x - x

⇒ Distance between police station and bank = 3x

From the calculation, 4x = 4 km

⇒ x = 1 km

Therefore, the distance between the police station and the bank = 3x = 3 × 1

⇒ Distance = 3 km

∴ The correct answer is option 4.