### APTITUDE – Problems on Pipes and Cisterns

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**Important Facts: **

1.INLET:A pipe connected with a tank or cistern or a reservoir, that fills it, it is known as Inlet.

OUTLET:A pipe connected with a tank or a cistern or a reservoir,emptying it, is known as Outlet.

2. i) If a pipe can fill a tank in x hours, then : part filled in 1 hour=1/x.

ii)If a pipe can empty a tank in y hours, then : part emptied in 1 hour=1/y.

iii)If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours( where y>x), then on opening both the pipes, the net part filled in 1 hour=(1/x -1/y).

iv)If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours( where x>y), then on opening both the pipes, the net part filled in 1 hour=(1/y -1/x).

v) If two pipes A and B can fill a tank in x hours and y hours respectively. If both the pipes are opened simultaneously, part filled by A+B in 1 hour= 1/x +1/y.

**Simple Problems**

**1)Two pipes A& B can fill a tank in 36 hours and 45 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?**

Sol: Part filled by A in 1 hour=1/36

Part filled by B in 1 hour= 1/45;

Part filled by (A+B)’s in 1 hour=1/36 +1/45= 9/180 =1/20

Hence, both the pipes together will fill the tank in 20 hours.

**2)Two pipes can fill a tank in 10 hours & 12 hours respectively. While 3rd pipe empties the full tank n 20 hours. If all the three pipes operate simultaneously,in how much time will the tank be filled?**

Sol: Net part filled in 1 hour=1/10 +1/12 -1/20

=8/60=2/15

The tank be filled in 15/2hours= 7 hrs 30 min

**3)A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 9 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?**

Sol: Net part filled in 1 hour= 1/4 -1/9= 5/36

Therefore the cistern will be filled in 36/5 hours or 7.2 hours.

**4)If two pipes function simultaneously, the reservoir will be filled in 12 days.One pipe fills the reservoir 10 hours faster than the other. How many hours does it take the second pipe to fill the reservoir.**

Sol: Let the reservoir be filled by the 1st pipe in x hours.

The second pipe will fill it in (x+10) hours

1/x + (1/(x+10))= 1/12

=> (2x+10)/((x)*(x+10))= 1/12

=> x=20

So, the second pipe will take 30 hours to fill the reservoir.

**5)A cistern has two taps which fill it in 12 min and 15 min respectively.There is also a waste pipe in the cistern. When all the three are opened,the empty cistern is full in 20 min. How long will the waste pipe take to empty the full cistern?**

Sol: Work done by a waste pipe in 1 min

=1/20 -(1/12+1/15)= -1/10 (-ve means emptying)

**6)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?**

Sol: Time taken by one tap to fill the half of the tank =3 hours

Part filled by the four taps in 1 hour=4/6=2/3

Remaining part=1 -1/2=1/2

Therefore, 2/3:1/2::1:x

or x=(1/2)*1*(3/2)=3/4 hours.

i.e 45 min

So, total time taken= 3hrs 45min.

**7)A water tank is two-fifth full. Pipe A can fill a tank in 10 min. And B can empty it in 6 min. If both pipes are open, how long will it take to
empty or fill the tank completely ?**

Sol: Clearly, pipe B is faster than A and So, the tank will be emptied.

Part to be emptied=2/5.

Part emptied by (A+B) in 1 min= 1/6 -1/10=1/15

Therefore, 1/15:2/5::1:x or x=((2/5)*1*15)=6 min.

So, the tank be emptied in 6 min.

**8)Bucket P has thrice the capacity as Bucket Q. It takes 60 turns for Bucket P to fill the empty drum. How many turns it will take for both the buckets P&Q, having each turn together to fill the empty drum?**

Sol: Let the capacity of P be x lit.

Then capacity of Q=x/3 lit

Capacity of the drum=60x lit

Required number of turns= 60x/(x+(x/3))= 60x*3/4x=45

**Complex Problems**

1)Two pipes can fill a cistern in 14 hours and 16 hours respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom it took 32min more to fill the cistern. When the cistern is full,in what time will the leak empty it?

Sol: Work done by the two pipes in 1 hour= 1/14+1/16=15/112

Time taken by these two pipes to fill the tank=112/15 hrs.

Due to leakage, time taken = 7 hrs 28 min+ 32 min= 8 hours

Therefore, work done by (two pipes + leak) in 1 hr= 1/8

work done by leak n 1 hour=15/112 -1/8=1/112

Leak will empty full cistern n 112 hours.

**2)Two pipes A&B can fill a tank in 30 min. First, A&B are opened. After
7 min, C also opened. In how much time, the tank s full.**

Sol: Part filled n 7 min = 7*(1/36+1/45)=7/20

Remaining part= 1-7/20=13/20

Net part filled in 1 min when A,B and C are opened=1/36 +1/45- 1/30=1/60

Now, 1/60 part is filled in 1 min.

13/20 part is filled n (60*13/20)=39 min

Total time taken to fill the tank=39+7=46 min

**3)Two pipes A&B can fill a tank in 24 min and 32 min respectively. If both the pipes are opened simultaneously, after how much time B should be closed so that the tank is full in 18 min. **

Sol: Let B be closed after x min, then part filled by (A+B) in x min + part filled by A in (18-x) min=1

x(1/24+1/32) +(18-x)1/24 =1

=> x=8

Hence B must be closed after 8 min.

**4)Two pipes A& B together can fill a cistern in 4 hours. Had they been opened separately, then B would have taken 6 hours more than A to fill the cistern. How much time will be taken by A to fill the cistern separately?**

Sol: Let the cistern be filled by pipe A alone in x hours.

Pipe B will fill it in x+6 hours

1/x + 1/x+6=1/4

Solving this we get x=6.

Hence, A takes 6 hours to fill the cistern separately.

**5)A tank is filled by 3 pipes with uniform flow. The first two pipes operating simultaneously fill the tan in the same time during which the tank is filled by the third pipe alone. The 2nd pipe fills the tank 5 hours faster than first pipe and 4 hours slower than third pipe. The time required by first pipe is :**

Sol: Suppose, first pipe take x hours to fill the tank then

B & C will take (x-5) and (x-9) hours respectively.

Therefore, 1/x +1/(x-5) =1/(x-9)

On solving, x=15

Hence, time required by first pipe is 15 hours.

**6)A large tanker can be filled by two pipes A& B in 60min and 40 min respectively. How many minutes will it take to fill the tanker from empty state if B is used for half the time & A and B fill it together for the other half?**

Sol: Part filled by (A+B) n 1 min=(1/60 +1/40)=1/24

Suppose the tank is filled in x minutes

Then, x/2(1/24+1/40)=1

=> (x/2)*(1/15)=1

=> x=30 min.

**7)Two pipes A and B can fill a tank in 6 hours and 4 hours respectively.If they are opened on alternate hours and if pipe A s opened first, in how many hours, the tank shall be full.**

Sol: (A+B)’s 2 hours work when opened alternatively =1/6+1/4 =5/12

(A+B)’s 4 hours work when opened alternatively=10/12=5/6

Remaining part=1 -5/6=1/6.

Now, it is A’s turn and 1/6 part is filled by A in 1 hour.

So, total time taken to fill the tank=(4+1)= 5 hours.

**8)Three taps A,B and C can fill a tank in 12, 15 and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternatively, the tank will be full in.**

Sol: (A+B)’s 1 hour’s work=1/12+1/15=9/60=3/20

(A+C)’s 1 hour’s work=1/20+1/12=8/60=2/15

Part filled in 2 hours=3/20+2/15=17/60

Part filled in 2 hours=3/20+2/15= 17/60

Part filled in 6 hours=3*17/60 =17/20

Remaining part=1 -17/20=3/20

Now, it is the turn of A & B and 3/20 part is filled by A& B in 1 hour.

Therefore, total time taken to fill the tank=6+1=7 hours

**9)A Booster pump can be used for filling as well as for emptying a tank. The capacity of the tank is 2400 m3. The emptying capacity of the tank is 10 m3 per minute higher than its filling capacity and the pump needs 8 minutes lesser to empty the tank than it needs to fill it. What is the filling capacity of the pump?**

Sol: Let, the filling capacity of the pump be x m3/min

Then, emptying capacity of the pump=(x+10) m3/min.

So,2400/x – 2400/(x+10) = 8

on solving x=50.

**10)A leak in the bottom of a tank can empty the full tan in 8 hr. An inlet pipe fills water at the rate of 6 lits a minute. When the tank is full,the inlet is opened and due to the leak, the tank is empty in 12 hrs.How many liters does the cistern hold?**

Sol: Work done by the inlet in 1 hr= 1/8 -1/12=1/24

Work done by the inlet in i min= (1/24)*(1/60)=1/1440

Therefore, Volume of 1/1440 part=6 lit

Volume of whole=(1440*6) lit=8640 lit.

**11)Two pipes A and B can fill a cistern in 37 ½ min and 45 minutes respectively. Both the pipes are opened. The cistern will be filled in
just half an hour, if the pipe B is turned off after:**

sol: Let B be turned off after x min. Then,

Part filled by (A+B) in x min+ part filled by A in (30-x)min=1

Therefore, x(2/75+1/45)+(30-x)(2/75)=1

11x/225 + (60-2x)/75=1

11x+ 180-6x=225

x=9.

So, B must be turned off after 9 minutes.

complex problem no. 2 chi completely hingal zaleli ahe. NOT AHE TO PROBLEM………

1. Three taps

A can fill tank in 6 hr.

B can fill tank in 9 hr.

C can empty tank in7.5 hr

Tap B is opened 3 hr after A is opened.

For how much time tap C should be open if the tank has to be filled in 6 hrs.

2. Tap A can fill a tank in 60 minutes , is opened at 6:00 p.m.

Tap B which can fill tank in 30 minute , opened at 6:10 p.m.

Tap R which can fill the tank in 20 minute is opened at 6:20 p.m.

At what time will the tank be full?

between 6 pm to 6:10 pm only A works so it full 1/60*10=1/6 part

between 6:10 pm to 6:20 pm only A & B works so (1/60+1/30)*10=1/2 part fill

total part fill 1/6+1/2=2/3

remain 1-2/3=1/3

after 6:20 all three tabs works so part which fill in 1 minute=1/60+1/30+1/20=1/10

1/10 part fill in=1 min

1/3 part fill in=10*1/3 min

10*60/3=200 sec

3 min 20 sec

so time at tank full=6:23:20

pls send problems on all chapters of Quantitative Aptitude forpractice purpose…..

to my mail address nvn220463@yahoo.co.in

A tank is 1/6th full.18 liters of water is added it becomes 7/15th. what is the tank capacity?

Two pipes A and B can fill a cistern in 24

minutes and 32 minutes respectively. If both

the pipes are opened together, then after how

many minutes B should be closed so that the

tank is full in 18 minutes

A leak in the bottom of a tank can empty the full tank in 8 hours.An inlet pipe fills water at the rate of 6 litres a minute . When the tank is full,the inlet is opened and due to the leak,the tank is empty in 12 hours. How many litres does the cistern hold?