Three pipes, A, B, and C are attached to a tank. A and B can fill it in 20 and 30 minutes respectively while C can empty it in 15 minutes.If A, B & C are kept open successively for 1 minute each, how soon will the tank be filled?
Answers
Answer
It will take 120 minutes to fill the tank
Explanation
Let A, B and C are the three pipes
A and B can fill it in 20 and 30 minutes respectively while C can empty it in 15 minutes.
We have to find the LCM(20, 30 , 15) = 60
So the total work is considered as 60
To calculate efficiency of each pipes in one minute
A ⇒ 60/20 = 3
B ⇒ 60/30 = 2
C ⇒ 60/15 = 1
First open pipe A for one minute 3 out of 60 filled
The open B for 1 minute , 2 out of 60 filled
After 2 minutes 3/60 + 2/60 = 5/60 of tank become filled
Again C is open 4/60 will empty
After 3 minutes, tank have 5/60 - 4/ 60 = 1/60 filled
In 3 minutes fill 1/60
So it will take 3 x 60 =120 minutes to fill the tank
Pipe A can fill the tank in 20 mins
⇒ 1 min = 1/20 of the tanks
Pipe B can fill the tank in320 mins
⇒ 1 min = 1/30 of the tanks
Pipe C can empty the tank in 15 mins
⇒ 1 min = 1/15 of the tanks
Pipe A, B and C are kept open successively for 1 minute each
Every 3 mins = 1/20 + 1/30 - 1/15 = 1/60 of the tank is filled
Find the time needed to fill the tank:
1/60 of the tank = 3 mins
60/60 of the tank = 3 x 60 = 180 mins
Answer: It takes 180 mins to fill the tank