A tank is filled with three pipes A, B, and C. Pipe A takes 18 hr. to fill 60% of the tank and Pipe B takes 8 hr. to fill 40% of the tank. Pipe A and Pipe C together fill 75% of the tank in 7.5hr. hr. Find the ratio of time taken to fill the tank by pipe A and B together to pipe B and pipe C together.

Solution

Since 60% of the tank filled up by Pipe A is 18 hr. Then the time taken to fill up the full tank is 30 hr. Similarly, 40 % of the tank filled by Pipe B is then the time taken to fill the full tank is 20hr. LCM of 20 and 30 is 600 litre of tank Therefore, efficiency of A is 20litres/hr and B is 30 litres/hr. units. Together A and C fill up 75% of the tank in 7.5 hrs. So, the time taken to fill up full tank by A and C together is 10 hours. So efficiency of A and C together to fill up the full tank   60 lt/hr Hence efficiency of C is 60-20 = 40 lt/hr. Efficiency of A and B together = 50lt/hr. Time taken to fill up the tank together by A and B is (600/50) = 12 hours The efficiency of B and C together to fill up the tank together is 70 lt/hr. Time taken to fill up the tank togerher by B and C is = 600/70 = 60/7 hr Required ratio = 12: (60/7)                            = 7:5