Pipes and Cistern
- Two pipes X and Y can fill a cistern in 24 minutes and 32 minutes respectively. If both the pipes are opened together, then after how much time (in minutes) should Y be closed so that the tank is full in 18 minutes ?
-
View Hint View Answer Discuss in Forum
If pipe Y be closed after t minutes, then
According to question ,18 + t = 1 24 32 ⇒ t = 1 - 18 = 1 - 3 = 1 32 24 4 4 ⇒ t = 32 = 8 minutes 4
We can find required answer with the help of given formula :
Here , p = 24, q = 32, t = 18Required time = 
q 
1 - t 
minutes p
Correct Option: B
If pipe Y be closed after t minutes, then
According to question ,18 + t = 1 24 32 ⇒ t = 1 - 18 = 1 - 3 = 1 32 24 4 4 ⇒ t = 32 = 8 minutes 4
We can find required answer with the help of given formula :
Here , p = 24, q = 32, t = 18Required time = q 1 - t minutes p Required time = 32 1 - 18 minutes 24 Required time = 32 1 - 3 4 Required time = 32 × 1 = 8 minutes 4
- A cistern is provided with two pipes A and B. A can fill it in 20 minutes and B can empty it in 30 minutes. If A and B be kept open alternately for one minute each, how soon will the cistern be filled ?
-
View Hint View Answer Discuss in Forum
As per the given in question , we have
Part of the tank filled in first two minutes = 1 - 1 = 3 - 2 = 1 20 30 60 60
Correct Option: C
As per the given in question , we have
Part of the tank filled in first two minutes = 1 - 1 = 3 - 2 = 1 20 30 60 60 ∴ Part of tank fillled in 114 minutes = 57 = 19 60 20
∴ Remaining part of cistern will be filled in 115th minute
- A water tank can be filled by a tap in 30 minutes and another tap can fill it in 60 minutes. If both the taps are kept open for 5 minutes and then the first tap is closed, how long will it take for the tank to be full ?
-
View Hint View Answer Discuss in Forum
On the basis of given details in question ,
Part of the tank filled by both taps in 5 minutes = 5 1 + 1 30 60 Part of the tank filled by both taps in 5 minutes = 5 2 + 1 = 5 × 3 = 1 60 60 4
Correct Option: D
On the basis of given details in question ,
Part of the tank filled by both taps in 5 minutes = 5 1 + 1 30 60 Part of the tank filled by both taps in 5 minutes = 5 2 + 1 = 5 × 3 = 1 60 60 4 Remaining part = 1 - 1 = 3 that is filled b second top. 4 4 ∴ Time taken = 3 × 60 = 45 minutes 4
- Three pipes A, B and C can fill a tank in 6 hours. After working together for 2 hours, C is closed and A and B can fill the remaining part in 7 hours. The number of hours taken by C alone to fill the tank is
-
View Hint View Answer Discuss in Forum
A, B and C together fill the tank in 6 hours.
∴ Part of the tank filled in 1 hour by (A + B + C) = 1 6 ∴ Part of the tank filled in 2 hours by all three pipes = 2 = 1 6 3 Remaining empty part = 1 - 1 = 2 3 3
This 2 /3 part is filled by (A + B).∴ Time taken by (A + B) to fill the fully empty tank = 7 × 3 = 21 hours 2 2
Correct Option: C
A, B and C together fill the tank in 6 hours.
∴ Part of the tank filled in 1 hour by (A + B + C) = 1 6 ∴ Part of the tank filled in 2 hours by all three pipes = 2 = 1 6 3 Remaining empty part = 1 - 1 = 2 3 3
This 2 /3 part is filled by (A + B).∴ Time taken by (A + B) to fill the fully empty tank = 7 × 3 = 21 hours 2 2 ∴ Part of tank filled by C in 1 hour = 1 - 2 = 7 - 4 = 3 = 1 6 21 42 42 14
∴ Required time = 14 hours.
- A tap can fill an empty tank in 12 hours and another tap can empty half the tank in 10 hours. It both the taps are opened simultaneously, how long would it take for the empty tank to be filled to half its capacity ?
-
View Hint View Answer Discuss in Forum
As per the given in question , we have
Part of the tank filled by pipe A in 1 hour = 1 12 Part of the tank emptied by pipe B in 1 hour = 1 20
Correct Option: A
As per the given in question , we have
Part of the tank filled by pipe A in 1 hour = 1 12 Part of the tank emptied by pipe B in 1 hour = 1 20 Part of the tank filled in 1 hour = 1 - 1 = 5 - 3 = 1 12 20 60 30
∴ Tank will be filled in 30 hours.
