Learn and practice Problems on pipes and cisterns with easy explaination and shortcut tricks. All questions and answers on pipes and cisterns covered for various Competitive Exams
Solve Problems:
1) A pipe can fill a tank in 6 hours and another pipe can empty the tank in 12 hours. If both the pipes are opened at the same time, the tank can be filled in
Part of the tank filled in one hour = Part of the tank emptied in one hour =1/12
Net part of the tank filled in one hour;
=1/6 -1/12
=(2-1)/12
=1/12
1/12 Part of the tank can be filled in one hour.
∴ The tank will be filled completely in 12 hours.
Solution 2:
Apply formula; =xy/(y-x)
X = 6 hours and Y = 12 hours
∴(6*12)/(12-6) = 12 hours
2) Three pipes A, B and C can fill a cistern in 8 minutes,12 minutes and 16 minutes respectively. What is the time taken by three pipes to fill the cistern when they are opened together?
Net part of the tank filled by A+B+C in one minute;
= 1/8 + 1/12 + 1/16
=13/48
13/48 Part of the cistern is filled in one minute.
∴ The whole tank will be filled in 48/13 = 3.7 minutes
3) Two pipes can fill a tank in 6 hours and 8 hours respectively. A third pipe can empty the same tank in 12 hours. If all the pipes start working together, how long it will take to fill the tank?
Part of the tank filled by two pipes in one hour = 1/6 + 1/8
Part of the tank emptied by the third pipe in one hour = 1/12
∴ Net part of the tank filled in one hour = 1/6 + 1/8 – 1/12
= 5/24
5/24 Part of tank can be filled in one hour
∴ The whole tank will be filled in 24/5 = 4.8 hours
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4) A tank can be filled in 10 hours. After a leak in its bottom, it takes 12 hours to fill the tank. Find the time taken by the leak to empty the full tank?
Part of the tank filled in one hour before the leak = 1/10
Part of the tank filled in one hour after the leak = 1/12
Part of the tank emptied in one hour by the leak = 1/10 – 1/12
=1/60
1/60 part of tank will be emptied in one hour by the leak
∴ The full tank will be emptied by the leak in 60 hours.
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5) Two pipes can fill a tank in 10 and 14 minutes respectively. A third pipe can empty the tank at the rate of10 liters/minute. If all the pipes working together can fill the empty tank in 8 minutes,what is the capacity of the tank?
Part of the tank filled by two pipes in one minute = 1/10 + 1/14
10 liters is emptied in 1 minute
X liters will be emptied in X/10 minutes
In X/10 minutes the whole tank will be emptied.
In one minute 10/X part of the tank will be emptied.
As per question;
6) A cistern can be filled by an inlet in 6 hours and can be emptied by an outlet in 8 hours. If the inlet and outlet are opened together, in what time the cistern can be filled?
Part of the tank filled by the inlet in one hour = 1/6 Part of the tank emptied by the outlet in one hour = 1/8 Net part of the tank filled in one hour = 1/6 – 1/8
=1/24
1/24 part of the tank is filled in one hour
∴ The whole tank will be filled in 24 hours.
7) 20 buckets can fill a tank when the capacity of each bucket is 12 liters. If the capacity of each bucket is 10 liters, find the number of buckets required to fill the tank.
20 buckets can fill the tank. So, capacity of tank = 20 * 12= 240 liters
New capacity of bucket = 10 liters
So, 10 liters can be poured into the tank by one bucket
240 liters will be poured by 1/10 * 240 = 24 buckets
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8) Two pipes working together can fill a fish tank in 12 minutes. If one pipe fills the fish tank 10 minutes faster than the second pipe, in what time the second pipe alone can fill the fish tank?
Let the first pipe fill the reservoir in X minutes
So, the second pipe will fill the reservoir in (X+10) minutes
As per question;
1/x + 1/(x+10) =1/12
12X +120 + 12X = X2 + 10X
X2 +10X 24X -120 = 0
X2 14X -120 =0
X2 – 20X+6X 120=0
X(X-20) +6(X-20) =0
(X+6) (X-20) = 0
X = 20
∴Second pipe will fill the reservoir in 20 + 10= 30 minutes
9) 25 outlets working 6 hours a day, can empty a reservoir in 10 days. If only 15 outlets are operational and work for 4 hours a day, in how many days the reservoir can be emptied?
Apply formula used in work and time problems; M1D1T1W2 = M2D2T2W1
M1= 25 outlets, D1=10 days, T1= 6 hours/day, W2 = to fill the reservoir
M2= 15 outlets, D2=? T2 = 4 hours/day, W1= to fill the reservoir
W1=W2
So we have; M1D1T1= M2D2T2
25*10*6=15*D2*4
1500 = 60 * D2
D2= 25 days
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10) Pipe A can fill a tank in 12 minutes whereas pipe A along with pipe B can fill the same tank in 8 minutes. In what time pipe B alone can fill the tank?
