Pipes and Cistern
- Three pipes A, B and C can fill a cistern in 10 hours, 12 hours and 15 hours respectively. First A was opened. After 1 hour, B was opened and after 2 hours from the start of A, C also opened . Find the time in which the cistern is just full ?
-
View Hint View Answer Discuss in Forum
[(A's 1 hour work) + (A + B)'s 1 hour work]
= (1/10) + [(1/10) + (1/12)] = 17/60
Remaining part = 1 - (17/60) = 43/60
Now, (A + B + C)'s 1 hour work = (1/10) + (1/12) + (1/15) = 1/4Correct Option: D
[(A's 1 hour work) + (A + B)'s 1 hour work]
= (1/10) + [(1/10) + (1/12)] = 17/60
Remaining part = 1 - (17/60) = 43/60
Now, (A + B + C)'s 1 hour work = (1/10) + (1/12) + (1/15) = 1/4
1/4 part is filled by 3 pipes in 1 hour.
43/60 part will be filled by them in 4 x (43/60) hrs. = 2 hours 52 min.
∴ Total time taken to fill the cistern = 4 hours 52 min.
- A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 litres a minute. When the tank is full, the inlet is opened and due to the leak the tank is empty in 8 hours. Find the capacity of the tank.
-
View Hint View Answer Discuss in Forum
From the given question ,
Part of tank filled by inlet pipe in 1 hour = 1 - 1 = 4 - 3 = 1 6 8 24 24
Correct Option: A
From the given question ,
Part of tank filled by inlet pipe in 1 hour = 1 - 1 = 4 - 3 = 1 6 8 24 24
Hence, if there is no leak, the inlet pipe will fill the tank in 24 hours.
∴ Capacity of the tank = 24 × 60 × 4 = 5760 litres
- There are 7 pipes attached with a tank out of which some are inlets and some are outlets. Every inlet can fill the tank in 10 h and every outlet can empty the tank in 15 h. When all the pipes are opened simultaneously, the tank is filled up in 28/11 h. Find the numbers of inlets and outlets. ?
-
View Hint View Answer Discuss in Forum
Let number of outlets be x
∴ Number of inlets = ( 7 - x )
Time taken to fill the tank when all the pipes are opened = 30/11h
Part of tank filled in 1 h when all the pipes are opened = 11/30 h
According to the question,
(7 - x)/10 - x/15 = 11/30Correct Option: A
Let number of outlets be x
∴ Number of inlets = ( 7 - x )
Time taken to fill the tank when all the pipes are opened = 30/11h
Part of tank filled in 1 h when all the pipes are opened = 11/30 h
According to the question,
(7 - x)/10 - x/15 = 11/30
⇒ {3(7 - x) - 2x}/30 = 11/30
⇒ 21 - 3x - 2x = 11
⇒ 5x = 10
∴ x = 2
Hence, number of outlets = 2 and number of inlets = 7 - 2 = 5
- A cistern can be filled up in 4 h by an inlet A. An outlet B can empty the cistern in 8 h. If both A and B are opened simultaneously, then after how much time will the cistern get filled?
-
View Hint View Answer Discuss in Forum
Part filled by A in 1 h = 1/4
Part emptied by B in 1 h = 1/8
Part filled by (A + B) In 1 h = 1/4+ ( -1/8 ) = 1/4 - 1/8 = (2 - 1)/8 = 1/8Correct Option: C
Part filled by A in 1 h = 1/4
Part emptied by B in 1 h = 1/8
Part filled by (A + B) In 1 h = 1/4+ ( -1/8 ) = 1/4 - 1/8 = (2 - 1)/8 = 1/8
∴ Required time to fill the cistern = 8
- Pipes A and B can fill a tank in 5 and 6 h, respectively. Pipe C can fill it in 30 h. If all the three pipes are opened together, then in how much time the tank will be filled up?
-
View Hint View Answer Discuss in Forum
Part filled by A in 1 h = 1/5
Part filled by B in 1 h = 1/6
Part filled by C in 1 h = 1/30Correct Option: B
Part filled by A in 1 h = 1/5
Part filled by B in 1 h = 1/6
Part filled by C in 1 h = 1/30
Net part filled by ( A + B + C ) in h 1 = ( 1/5 + 1/6 + 1/30 )
= (6 + 5 + 1)/30 = 12/30 = 2/5
∴ Required time to fill the tank = 5/2 = 21/2 h
