In the following question, two statements are numbered as A and B. On solving these statements, we get quantities A and B respectively. Solve both quantities and choose the correct option. Quantity A: Pipe A takes thrice the time taken by Pipe B to fill a tank. Together they can fill the tank in 15 hours, tank A and B is opened together for 4 hours and then Pipe A is closed and after 2 more hours Pipe B is closed and an outlet Pipe C is opened which when working alone can empty the tank in 10 hours. Calculate the time taken by C to empty the tank. Quantity B: A pipe A can fill the tank in 10 hours another pipe B can fill the tank in 15 hours and with the help of third pipe C they can fill the tank in 5 hours. Pipe A is opened for 4 hours then it is closed, pipe B is closed 3 hours before filling of tank and tank C is opened the whole time. Calculate the time taken to fill the tank. Correct Answer Quantity A Quantity A: Let the time taken by B be x Tank filled by B in 1 hour = 1/x Then, time taken by A is 3x Tank filled by B in 1 hour = 1/x ∴ According to question ⇒ (1/x) + (1/3x) = 1/15 ⇒ 4/3x = 1/15 ⇒ x = 20 Pipe B takes 20 hours to fill the tank Pipe A takes = 20 × 3 = 60 hours to fill the tank Now, pipe B is opened for 4 hours and A is opened for 6 hours ⇒ 4/20 + 6/60 = 1/5 + 1/10 = 3/10 An outlet pipe C can empty the tank alone in 10 hours Tank emptied by C in 1 hour = 1/10 ⇒ Time taken to empty the tank = (3/10) – (1/10) = 2/10 = 1/5 ∴ Tank will be emptied in 5 hours Quantity B: Time taken by A to fill the tank = 10 hours Tank filled by A in 1 hour = 1/10 Time taken by B to fill the tank = 15 hours Tank filled by B in 1 hour = 1/15 Let the time taken by C be x Tank filled by C in 1 hour = 1/x Together they can fill the tank in 5 hours ⇒ (1/10) + (1/15) + (1/x) = 1/5 ⇒ 1/10 + 1/15 – 1/5 = 1/x ⇒ 1/x = 1/30 Time taken by B to fill the tank = 30 hours Pipe A is opened for 4 hours then it is closed, pipe B is closed 3 hours before filling of tank and tank C is opened the whole time Let the time taken in which tank will completely filled be x ⇒ 4/ 10 + (x – 3)/15 + x/30 = 1 ⇒ (3x + 6)/30 = 1 ⇒ 3x = 24 ⇒ x = 8 ∴ Time taken to fill the tank 8 hours Hence Quantity A < Quantity B