Q1)-A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?
Q2)-One pipe can fill a tank four times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in:
Q3)-Two pipes A and B can fill a tank in 20 and 30 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?
Q4)-A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 liters a minute. When the tank is full, the inlet is opened and due to the leak, the tank is empty in 24 hours. How many liters does the tank hold?
Q5)-A cistern can be filled by a tap in 12 hours and by the other tap in 9 hours. If both taps are opened together how long will it take to fill the cistern?
Q6)-A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 4 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold?
Q7)-One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in
Q8)-Two pipes function simultaneously the reservoir will be filled in 12 hours. One pipe fills reservoir 10 hours faster than the other. How many hours does the faster pipe take to fill the reservoir?
Q9)-A cistern can be filled in 9 hours but due to a leak at its bottom it takes 10 hours. If the cistern is full, then the time that the leak will take to make it empty will be ?
Q10)-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 liters 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 liters does the cistern hold?
20 hours
25 hours
35 hours
Cannot be determined
Ans.- C
Suppose pipe A alone takes x hours to fill the tank.
Then, pipes B and C will take x/2 and x/4 hours respectively to fill the tank.
1/x + 2/x + 4/x = 1/5
7/x = 1/5
x = 35 hours
Suppose pipe A alone takes x hours to fill the tank.
Then, pipes B and C will take x/2 and x/4 hours respectively to fill the tank.
1/x + 2/x + 4/x = 1/5
7/x = 1/5
x = 35 hours
Q2)-One pipe can fill a tank four times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in:
180 min
144 min
126 min
114 min
Ans.- A
The faster pipe is equivalent to 4 slower pipes together.
5 slower pipes together can fill the tank in 36 minutes.
Therefore, 1 slower pipe can fill the tank in 36×5=180 minutes.
The faster pipe is equivalent to 4 slower pipes together.
5 slower pipes together can fill the tank in 36 minutes.
Therefore, 1 slower pipe can fill the tank in 36×5=180 minutes.
Q3)-Two pipes A and B can fill a tank in 20 and 30 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?
12 min
14 min
15 min
18 min
Ans.- A
Part filled by A in 1 min = 1/20
Part filled by B in 1 min =1/30
Part filled by (A + B) in 1 min = (1/20 + 1/30 )=1/12
Both pipes can fill the tank in 12 minutes.
Part filled by A in 1 min = 1/20
Part filled by B in 1 min =1/30
Part filled by (A + B) in 1 min = (1/20 + 1/30 )=1/12
Both pipes can fill the tank in 12 minutes.
Q4)-A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 liters a minute. When the tank is full, the inlet is opened and due to the leak, the tank is empty in 24 hours. How many liters does the tank hold?
4010 litre
2220 litre
1920 litre
2020 litre
Ans.- C
water filled by the inlet pipe in 24 hours = water emptied by the leak in 24−6=18 hours.
Therefore, water emptied by the leak in 6 hours = water filled by the inlet pipe in 8 hours
i.e., capacity of the tank
= water filled by the inlet pipe in 8 hours
=8×60×4=1920 litre.
water filled by the inlet pipe in 24 hours = water emptied by the leak in 24−6=18 hours.
Therefore, water emptied by the leak in 6 hours = water filled by the inlet pipe in 8 hours
i.e., capacity of the tank
= water filled by the inlet pipe in 8 hours
=8×60×4=1920 litre.
Q5)-A cistern can be filled by a tap in 12 hours and by the other tap in 9 hours. If both taps are opened together how long will it take to fill the cistern?
6/7 hours
36/7 hours
7/36 hours
None of these
Ans.- B
Time taken by the 1st tap to fill the cistern = 12 hours
Therefore, work done by the 1 st tap in 1 hour = 1/12
Time taken by the 2nd tap to fill the cistern = 9 hours.
Therefore, work done by the 2nd tap in 1 hour = 1/9
Therefore, work done by the both taps in 1 hour = 1/12 + 1/9
= (3 + 4)/36
= 7/36
Therefore, both taps will fill the cistern in = 36/7 hours.
Time taken by the 1st tap to fill the cistern = 12 hours
Therefore, work done by the 1 st tap in 1 hour = 1/12
Time taken by the 2nd tap to fill the cistern = 9 hours.
Therefore, work done by the 2nd tap in 1 hour = 1/9
Therefore, work done by the both taps in 1 hour = 1/12 + 1/9
= (3 + 4)/36
= 7/36
Therefore, both taps will fill the cistern in = 36/7 hours.
Q6)-A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 4 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold?
480 liters
600 liters
720 liters
800 liters
Ans.- A
1/x - 1/20 = -1/24
x = 120
120 x 4 = 480
1/x - 1/20 = -1/24
x = 120
120 x 4 = 480
Q7)-One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in
144 mins
140 mins
136 mins
132 mins
Ans.- A
Let the slower pipe alone fill the tank in x minutes
then faster will fill in x/3 minutes.
Part filled by slower pipe in 1 minute = 1/x
Part filled by faster pipe in 1 minute = 3/x
Part filled by both in 1 minute = 1/x + 3/x =1/36
4/x= 1/36
x = 144 mins
Let the slower pipe alone fill the tank in x minutes
then faster will fill in x/3 minutes.
Part filled by slower pipe in 1 minute = 1/x
Part filled by faster pipe in 1 minute = 3/x
Part filled by both in 1 minute = 1/x + 3/x =1/36
4/x= 1/36
x = 144 mins
Q8)-Two pipes function simultaneously the reservoir will be filled in 12 hours. One pipe fills reservoir 10 hours faster than the other. How many hours does the faster pipe take to fill the reservoir?
25 hrs
28 hrs
20 hrs
35 hrs
Ans.- C
1/x + 1/(x + 10) = 1/12
x = 20
1/x + 1/(x + 10) = 1/12
x = 20
Q9)-A cistern can be filled in 9 hours but due to a leak at its bottom it takes 10 hours. If the cistern is full, then the time that the leak will take to make it empty will be ?
20 hours
19 hours
90 hours
80 hours
Ans.- C
Part filled without leak in 1 hour = 1/9
Part filled with leak in 1 hour = 1/10
Work done by leak in 1 hour = (1/9) - (1/10) = 1/ 90
We used subtraction as it is getting empty. So total time to empty the cistern is 90 hours
Part filled without leak in 1 hour = 1/9
Part filled with leak in 1 hour = 1/10
Work done by leak in 1 hour = (1/9) - (1/10) = 1/ 90
We used subtraction as it is getting empty. So total time to empty the cistern is 90 hours
Q10)-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 liters 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 liters does the cistern hold?
7580
7960
8290
8640
Ans.- D
Work done by the inlet in 1 hour = 1/8 - 1/12 = 1/24
Work done by the inlet in 1 min. = 1/24 x 1/60 = 1/1440
Given, volume of 1/1440 part = 6 liters.
⇒ Volume of whole = 6 * 1440 = 8640 liters.
Work done by the inlet in 1 hour = 1/8 - 1/12 = 1/24
Work done by the inlet in 1 min. = 1/24 x 1/60 = 1/1440
Given, volume of 1/1440 part = 6 liters.
⇒ Volume of whole = 6 * 1440 = 8640 liters.
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