pipes A& B can fill a tank in 16hours and 24hours respectively and pipe C alone can empty the full tank in X hours all the pipes were opened together at 10:30am but C closed at 2:30 pm .if the tank was full at 8:30pm on the same day ,than what is the value of X?
Answers
Answer: 96 Hours.
Step-by-step explanation:
Part of the tank filled in one hour by pipe A = 1/16
Part of the tank filled in one hour by pipe B = 1/24
Pipe C, can empty the full tank in X hours,
Part of the tank emptied in one hour by pipe C = 1/X
When all the three pipes are opened in the beginning,
Net part filled in one hour = (1/15)+(1/20)-(1/X) = 1/16 + 1/24 - 1/X
In 4 hours (from 10.30 am to 2.30 pm) , the part filled, F1 = 4 x (1/16 + 1/24 - 1/X )
= 4/16 + 4/24 - 4/X
= 10/24 - 4/X
= 5/12 - 4/X
After 4 hours, pipes A and B together take 6 (from 2.30 pm TO 8.30 pm) hours to fill the remaining part,
Part filled by A and B in one hour = (1/16)+(1/24) = 5/48
Part filled by A and B in 6 hours F2 = 6 x (5/48) = 5/8
Total part filled = F1 + F2, which shall be equal to 1
(5/12 - 4/X) + 5/8 =1
100/96 - 1 = 4/X
X = 96 Hours