An empty tank be filled with an inlet pipe ‘A’ in 42 minutes. After 12 minutes an outlet pipe ‘B’ is opened which can empty the tank in 30 minutes. After 6 minutes another inlet pipe ‘C’ opened into the same tank, which can fill the tank in 35 minutes and the tank is filled. Find the time taken to fill the tank?
Answers
Answer:
58.5 min
Step-by-step explanation:
An empty tank be filled with an inlet pipe ‘A’ in 42 minutes. After 12 minutes an outlet pipe ‘B’ is opened which can empty the tank in 30 minutes. After 6 minutes another inlet pipe ‘C’ opened into the same tank, which can fill the tank in 35 minutes and the tank is filled. Find the time taken to fill the tank?
tank be filled with an inlet pipe ‘A’ in 42 minutes
Pipe A can fill in 1 min = 1/42
pipe A in 12 minutes can fill in = 12/42 = 2/7
Pipe b can empty tank in 30 mins
pipe b can can empty in 1 min = 1/30
When A & B both together
can empty in 1 min = 1/30 - 1/42 = (7 - 5)/210 = 1/105
in 6 mins empties = 6/105 = 2/35
After 12 + 6 = 18 mins Tank is filled
= 2/7 - 2/35
= 8/35
Tank remained to fill = 1 - 8/35 = 27/35
C can fill in 35 min
C can fill in 1 min = 1/35
A , B & C together can fill in 1 min 1/35 - 1/105 = 2/105
2/105 is filled in 1 min
1 is filled in 105/2 min
27/35 filled in = (27/35) * (105/2) = 81/2 = 40.5 min
Total Time = 18 + 40.5 = 58.5 min