Pipes and Cistern
- A tap can fill a tank in 6 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely ?
-
View Hint View Answer Discuss in Forum
A tap can fill the tank in 6 hours. In filling the tank to its half, time required = 3 hours.
Remaining part = 1 2
∵ 1 tap takes 6 hours to fill the tank∴ Time taken by 4 taps take to fill 1 / 2 of the tank = 6 × 1 = 3 hours 4 2 4
Correct Option: D
A tap can fill the tank in 6 hours. In filling the tank to its half, time required = 3 hours.
Remaining part = 1 2
∵ 1 tap takes 6 hours to fill the tank∴ Time taken by 4 taps take to fill 1 / 2 of the tank = 6 × 1 = 3 hours 4 2 4 ∴ Total time = 3 + 3 4 Total time = 3 3 hours 4
Therefore , Total time = 3 hours 45 minutes
-
Two pipes A and B can fill a cistern in 37 1 minutes and 45 minutes respectively. Both 2
pipes are opened.The cistern will be filled just in half an hour, if the pipe B is turned off after :
-
View Hint View Answer Discuss in Forum
On the basis of given details in question ,
Pipe A fills the tank in 75/2 minutes.∴ Part of the tank filled by A in 30 minutes = 2 × 30 = 4 75 5 Remaining part = 1 - 4 = 1 5 5
Correct Option: D
On the basis of given details in question ,
Pipe A fills the tank in 75/2 minutes.∴ Part of the tank filled by A in 30 minutes = 2 × 30 = 4 75 5 Remaining part = 1 - 4 = 1 5 5
Now, 1 part is filled by pipe B in 45 minutes∴ 1 / 5 part is filled in = 45 × 1 = 9 minutes 5
Hence, the pipe B should be turned off after 9 minutes.
- A tank is fitted with two taps. The first tap can fill the tank completely in 45 minutes and the second tap can empty the full tank in one hour. If both the taps are opened alternately for one minute, then in how many hours the empty tank will be filled completely ?
-
View Hint View Answer Discuss in Forum
As per the given in question , we have
Part of the tank filled in one minute = 1 - 1 45 60 Part of the tank filled in one minute = 4 - 3 = 1 180 180 ∵ 1 part is filled in 1 minute 180 ∴ 1 - 1 = 44 part is filled in 2 × 180 × 44 = 352 minutes i.e. 5 hours 52 minutes 45 45 45
Correct Option: D
As per the given in question , we have
Part of the tank filled in one minute = 1 - 1 45 60 Part of the tank filled in one minute = 4 - 3 = 1 180 180 ∵ 1 part is filled in 1 minute 180 ∴ 1 - 1 = 44 part is filled in 2 × 180 × 44 = 352 minutes i.e. 5 hours 52 minutes 45 45 45 Remaining 1 part will be filled in 1 minute. 45
∴ Total time taken = 5 hours 53 minutes
- A tank can be filled by two pipes in 20 minutes and 30 minutes respectively. When the tank was empty, the two pipes were opened. After some time, the first pipe was stopped and the tank was filled in 18 minutes. After how much time of the start was the first pipe stopped?
-
View Hint View Answer Discuss in Forum
Let the first pipe be closed after t minutes .
According to question ,∴ t + 18 = 1 20 30 ⇒ t = 1 - 18 = 1 - 3 = 2 20 30 5 5 ⇒ t = 2 × 20 = 8 minutes; 5
Second method to solve this question :
Here, p = 20, q = 30, t = 18
[∵ first pipe is closed]Required time = 
p 
1 - t 
q
Correct Option: B
Let the first pipe be closed after t minutes .
According to question ,∴ t + 18 = 1 20 30 ⇒ t = 1 - 18 = 1 - 3 = 2 20 30 5 5 ⇒ t = 2 × 20 = 8 minutes; 5
Second method to solve this question :
Here, p = 20, q = 30, t = 18
[∵ first pipe is closed]Required time = p 1 - t q Required time = 20 1 - 18 30 Required time = 20 × 12 = 8 minutes; 30
- A tap takes 36 hours extra to fill a tank due to a leakage equivalent to half of its inflow. The inflow can fill the tank in how many hours?
-
View Hint View Answer Discuss in Forum
Let the inflow fill the tank in t hours.
According to question ,
[leakage being half of inflow]∴ 1 - 1 = 1 t 2t 36 ⇒ 2 - 1 = 1 2t 36
Correct Option: D
Let the inflow fill the tank in t hours.
According to question ,
[leakage being half of inflow]∴ 1 - 1 = 1 t 2t 36 ⇒ 2 - 1 = 1 2t 36
⇒ 2t = 36⇒ t = 36 = 18 hours 2
