21). There is a crack at the bottom of a tank. Before the crack appeared, Pipe A could fill the tank in 2 hours. Now it takes half an hour longer. How long will the crack take to empty a full tank when Pipe A is kept closed?
A). 10 hours 
B). 12 hours 
C). 15 hours 
D). 9 hours 
Correct Answer: 10 hours
Before the crack appeared, Pipe A could fill \( \Large \frac{1}{2} \) the tank in an hour.
Now it takes 2 hours 30 minutes to fill the tank. That is \( \Large \frac{5}{2} \) hours.
Hence, it fills \( \Large \frac{2}{5} \)th of the tank every hour.
The crack at the bottom accounts for this reduction in the amount.
The crack, therefore, drains \( \Large \frac{1}{2}\frac{2}{5}=\frac{54}{10}=\frac{1}{10} \)th of the tank every hour.
As the crack drains a tenth of the tank every hour, it will drain the entire tank in 10 hours if Pipe A is kept closed.

22). Pipe A can fill a tank in 14 hours and Pipe B can fill the same tank in 16 hours. Because of a crack at the bottom of the tank, it takes 32 minutes more to fill the empty tank when both the pipes are kept open simultaneously. How long will the crack at the bottom take to drain a full tank if Pipes A and B are kept closed?
A). 108 hours 
B). 112 hours 
C). 120 hours 
D). 130 hours 
Correct Answer: 112 hours
Pipe A and Pipe B together can fill \( \Large \frac{1}{14}+\frac{1}{16}=\frac{15}{112} \)th of the tank in an hour. That is they take \( \Large \frac{112}{15} \) hours to fill the tank.
Because of the crack, they will take 32 more minutes or \( \Large \frac{32}{60} \)hours more to fill the tank.
That is \( \Large \frac{112}{15}+\frac{32}{60}= \frac{448 + 32}{60} = \frac{480}{60}= 8 hours \) to fill the tank. Or \( \Large \frac{1}{8} \)th of tank gets filled in an hour.
The crack, therefore, drains \( \Large \frac{15}{112}\frac{1}{8}=\frac{154}{112}=\frac{1}{112} \)th of the tank every hour.
Therefore, the leak alone will take 112 hours to empty the tank.

23). 3 small pumps and a large pump are filling a tank. Each of the three small pumps works at 2/3rd the rate of the large pump. If all 4 pumps work together, they should fill the tank in what fraction of the time that would have taken the large pump alone?
A). \( \Large \frac{1}{5} \)th of the time 
B). \( \Large \frac{1}{4} \)th of the time 
C). \( \Large \frac{1}{3} \)rd of the time 
D). \( \Large \frac{1}{6} \)th of the time 
Correct Answer: \( \Large \frac{1}{3} \)rd of the time
Rate of filling by each small pump = \( \Large \frac{2}{3} \)rd of that of large pump.
Therefore, rate of filling by 3 small pumps = \( \Large 3 \times \frac{2}{3} \) of that of large pump = twice of that of large pumps.
If all 4 pumps work together, they will fill as much water as that by 3 large pumps.
Therefore, time taken by 4 pumps = \( \Large \frac{1}{3} \) of the time taken by large pump.

24). Pipe A which can fill a tank in 20 minutes is kept open for 5 minutes when the tank is empty. Then Pipe B which can fill the tank in 30 minutes is also opened. How long after Pipe A is opened will the tank be full?
A). 12 minutes 
B). 17 minutes 
C). 16 minutes 
D). 14 minutes 
Correct Answer: 14 minutes
Pipe A fills \( \Large \frac{1}{20} \)th of the tank every minute. ln 5 minutes, it will fill \( \Large 5 \times \frac{1}{20} = \frac{1}{4} \)th of the tank.
After 5 minutes, Pipe B is also opened.
Together, Pipe A and Pipe B fill \( \Large \frac{1}{20}+\frac{1}{30}=\frac{3+2}{60}=\frac{1}{12} \)th of the tank every minute.
Together the pipes will fill an empty tank in 12 minutes.
As Pipe A alone had filled 1/4th of the tank by the time Pipe B was opened, only 3/4ths of the tank needs to be filled when the 2 pipes are working together.
To fill 3/4ths the tank, the two pipes will take \( \Large \frac{3}{4} \times 12 = 9\ min. \)
And, the total time taken = 5 + 9 = 14 minutes.

25). Pipe A alone can fill a tank in 8 minutes. Pipe B alone can fill the same tank in 12 minutes. Both the pipes are opened together when the tank is empty. However, Pipe B is closed 3 minutes before the tank is full. In what time did the tank get filled?
A). 6 minutes 
B). 8 minutes 
C). 10 minutes 
D). 12 minutes 
Correct Answer: 6 minutes
A Pipe A is kept open till the tank gets filled.
Let the time for which Pipe A is kept open = t minutes
Therefore, pipe B was kept open for (t  3) minutes only.
Pipe A fills \( \Large \frac{1}{8} \)th of the tank in a minute and pipe B fills \( \Large \frac{1}{12} \)th of the tank every minute.
Together (A was open for t minutes and B for t3 minutes) pipe A and pipe B fill ONE full tank
i.e. \( \Large \frac{t}{8}+\frac{t3}{12}=1\ or\ \frac{3t+2t6}{24}\ or\ 5t = 30\ or\ 5=6 minutes \)

26). Pipe A alone can fill a tank in 12 minutes and Pipe B can fill the same tank in 15 minutes. Pipe C which is at the bottom of the tank can drain the tank at the rate of 22 litres/minute. If all three pipes are kept open together when the tank is full, the tank gets emptied in one hour. What is the capacity of the tank?
A). 140Ltrs. 
B). 132 Ltrs. 
C). 150 Ltrs. 
D). 146 Ltrs. 
Correct Answer: 132 Ltrs.
Let C be the lime that Pipe C takes to empty the tank when Pipe A and Pipe B are closed.
Pipe A + Pipe B  Pipe C kept Open together results in a full tank getting emptied in 1 hour (60 min.)
\( \Large \frac{1}{12}+\frac{1}{15}\frac{1}{C} = \frac{1}{60} \) (negative sign indicates that the tank is getting emptied) or \( \Large \frac{1}{12}+\frac{1}{15}\frac{1}{C}=\frac{1}{C}\ or\ C = 6\ minutes \)
If Pipe C can empty the tank in 6 minutes and it drains water at the rate of 22 liters/minute, then the capacity of the tank = \( \Large 6 \times 22 \) = 132 liters.

27). Pipe A can fill a tank in 4 minutes. Pipe B can fill the same tank in 8 minutes. Pipe C at the bottom of the tank can drain the tank completely in 6 minutes. If all three pipes are kept open together when the tank is empty and pipe C is shut after 3 minutes, in how many minutes will the tank be full after Pipe C is shut?
A). 3 minutes 
B). 5 minutes 
C). 1 minute 
D). 2 minutes 
Correct Answer: 1 minute
During the first 3 minutes all 3 pipes are open. i.e.\( \Large \left(\frac{3}{4}+\frac{3}{8}\frac{3}{6}\right) \)th = \( \Large \frac{18+912}{24}=\frac{15}{24} \)th of the lank will be full.
Then Pipe C is shut. Pipe A and Pipe B will fill \( \Large \frac{1}{4}+\frac{1}{8}=\frac{3}{8} \)th of the tank every minute.
As \( \Large \frac{15}{24} \)th of the tank is already full, Pipes A and B together have to fill
= \( \Large 1  \frac{15}{24}=\frac{9}{24}=\frac{3}{8} \)th of the tank.
Therefore, it will take another 1 minute, after Pipe C is shut, to fill the tank.

28). Pipe A fills a tank in 24 minutes. Pipe B can fill the same tank 7 times as fast as Pipe A. If both the pipes are kept open when the tank is empty, when will the tank be full?
A). 5 minutes 
B). 2 minutes 
C). 4 minutes 
D). 3 minutes 
Correct Answer: 3 minutes
Pipe B will fill the tank in \( \Large \frac{24}{7} \) minutes as it is 7 times as fast as Pipe A.
Together, the two pipes will fill \( \Large \frac{1}{24}+\frac{7}{24}=\frac{8}{24}=\frac{1}{3} \)rd of the tank in a minute.
So, it will take 3 minutes for the tank to overflow.

29). Pipe A can fill a tank in 10 minutes. Pipe B can fill the same tank in 15 minutes. Pipe C at the bottom of the tank is a waste pipe for emptying the tank. After opening Pipe A and Pipe B, a man returns when the tank should have been full. However, he finds that Pipe C was also kept open and shuts it and the tank overflows in the next 2 minutes. How many minutes will Pipe C take to empty the tank if Pipes A and B are kept shut?
A). 18 minutes 
B). 16 minutes 
C). 14 minutes 
D). 12 minutes 
Correct Answer: 18 minutes
Pipe A and Pipe B together fill \( \Large \frac{1}{10}+\frac{1}{15}=\frac{5}{30}=\frac{1}{6} \)th of the tank in a minute
Therefore, the man would have returned to the tank 6 minutes after opening the taps hoping to see the tank full. However, he finds Pipe C open and shuts it immediately.
After shutting Pipe C, the tank was full in 2 minutes.
Therefore, in the last two minutes \( \Large \frac{1}{6} \times 2=\frac{1}{3} \)rd of the tank would have been filled by Pipe A and Pipe B.
This is the quantum of water that Pipe C would have drained during the first 6 minutes.
lf Pipe C drained 1/3rd of the tank in 6 minutes, then it will take 18 minutes to drain the entire tank.

30). A tank is fitted with 8 pipes, some that fill the tank and others that empty the tank. Each of the fill pipes fills the tank in 8 hours, while each of the waste pipes empties it in 6 hours. lf all the pipes are kept open when the tank is full, the tank will be completely drained in 6 hours. How many of these 8 pipes are fill pipes?
A). 6 fill pipes 
B). 4 fill pipes 
C). 7 fill pipes 
D). 3 fill pipes 
Correct Answer: 4 fill pipes
Let the number of fill pipes be 'n'. Therefore, there will be (8  n) waste pipes.
Each fill pipe fills \( \Large \frac{1}{8} \)th of the tank in an hour. So, "n" fill pipes will fill \( \Large \frac{n}{8} \)th of the tank in an hour.
Each waste pipe drains \( \Large \frac{1}{6} \)th of the tank in a hour.
So, \"8  n\" waste pipes will drain \( \Large \frac{8n}{6} \)th of the tank in an hour.
Keeping these 8 pipes open results in \( \Large \frac{1}{6} \)th of the tank being drained every hour.
Hence, \( \Large \frac{n}{8}\frac{8n}{6}= \frac{1}{6} \)
Solving for n, we get n = 4.
Therefore, there are 4 fill pipes and 4 waste pipes.
