Explanation / Important formulas:
Inlet: A pipe connected with a tank or a cistern or a reservoir that fills it, is known as an inlet.
Outlet: A pipe connected with a tank or cistern or reservoir emptying it, is known as an outlet.
 If a pipe can fill a tank in x hours, then:part filled in 1 hour = 1 / x
 If a pipe can empty a tank in y hours, then:part emptied in 1 hour = 1
 If a pipe can fill a tank in y/x hours and another pipe can empty the full tank in y hours (where y > x), then on opening both the pipes, then the net part filled in 1 hour = (1/x – 1/y)
 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, then the net part emptied in 1 hour = (1/y – 1/x)
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Pipes and Cisterns  Test
Pipes and cisterns  Question and Answers
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Question 1

A

12minutes

B

13.5 minutes

C

15minutes

D

14.5 minutes

1/60th of the tank is emptied by pipe C in 1 minutes
Part of tank filled in the first 6 minutes = 6*[(1/20)+(1/30)] = ½
When all pipes are opened, part of tank filled in 1 minutes = (1/12)(1/60) = 1/15
Time required to fill the remaining ½ of the tank = (1/2) / (1/15) = 7.5
Total time = 6+7.5 = 13.5 minutes
Question 2

A

12

B

15

C

20

D

18

= (1/20) + (1/10) – (1/15) = 1/12
Time taken to fill the tank = 12 minutes
Question 3

A

7 liters

B

5 liters

C

3.5 liters

D

2.5 liters

Part of tank emptied by Q in an hour = 1/1.5 = 2/3
Part of tank filled by R in an hour = ½
Part of tank filled by S in an hour = 1/ 2.5 = 2/5
Part of tank emptied in an hour = (1+ (2/3))  (1/2 + (2/5)) = 23/30
Water remaining in the tank = 15*7/30 = 3.5 liters
Question 4

A

180 minutes

B

167 minutes

C

200 minutes

D

178 minutes

Part filled in 165 minutes = (165/3) * (1/60) = 55/60
Part filled in 167 minutes = (55/60) + (1/20) + (1/30) = 60/60 = 1
The tank is filled in 167 minutes
Question 5

A

30 minutes

B

45 minutes

C

40 minutes

D

25 minutes

Part of tank filled by B in a minutes =1/75
Let pipe B be closed after x minutes
Part of tank filled in x minutes= x*[(1/60)+(1/75)]
= 9x / 300
Part of tank filled in (40x) minutes = [(40x)*(1/60)]
= (40x) / 60
(9x / 300) + ((40  x) / 60) = 1
4x = 100
X= 25
Question 6

A

60 minutes

B

40 minutes

C

30 minutes

D

20 minutes

Part of the tank filled by A and B = (1/60) + (1/x) = (1/20)
Solving this, x= 30
Question 7

A

10 minutes

B

7/6 hours

C

6/7 hours

D

7hours

1hr 10 min = 1+(1/6) = 7/6 hrs
1 (1/x) = 1/ (7/6) = 6/7
Part of tank leaked in an hour = 16/7 = 1/7
The leak takes7 hours to drain all the water
Question 8

A

6 minutes

B

12 minutes

C

12.5 minutes

D

24 minutes

Part of the tub filled in the next 2 minutes = 2*1/15 = 2/15
Part of the filled in 4 minutes = (1/5) +(2/15) =1/3
Time required to fill the tub = 3*4 = 12 minutes
Question 9

A

7 minutes

B

14 minutes

C

3.5 minutes

D

28 minutes

(7/2x) = ¼
x=14
x /2 = 7
Question 10

A

480 liters

B

360 liters

C

300 litres

D

240 liters

Part of the tank emptied by the outlet in a minute = 1 / (5*60) = 1/300
Part of the tank filled in the first 30 minutes = 30*[(1/x)  (1/300)]
= (300  x) / 10x
Part of the tank filled in the next 36minutes = 36 * (1/x)
1 – [(300  x) / 10 x] = 36 / x
Solving, x= 60
Capacity of tank = 60 * 5 = 300 liters
Question 11

A

10hours

B

5 hours

C

9 hours

D

6 hours

5x= 1+2+3+ .......+x
5x = x(x+1) / 2
X= 9 hours
Question 12

A

15 minutes

B

30 minutes

C

12 minutes

D

10 minutes

Part of tank filled by B in 1 minute = (1/20) / 3 = 1/60
Part of tank filled by them together in 1 min = (1/20) + (1/60) = 1/15
They take 15 min to fill the tank
Question 13

A

20 minutes

B

1 hour

C

30 minutes

D

60 minutes

Part of bucket filled by the tap in 1 minute =1/10
(1/10) – (1/x) = (1/12)
X = 60 minutes
Question 14

A

28

B

20

C

15

D

24

No. of buckets needed = 288 / 12 = 24
Question 15

A

100 minutes

B

75 minutes

C

90 minutes

D

80 minutes

Pipe A is closed before 30 minutes of overflow
Only pipe B was opened
Part of tank filled by pipe B in 30 minutes = ¼
The remaining 3/4th of the tank was filled by pipes A and B
To fill 3/4th of the tank together, 1 hour is taken
Time for overflow = 1 hours + 30 minutes
= 90 minutes
Question 16

A

3 hours

B

30 hours

C

10 hours

D

33 hours

= (1/6) +(1/10) + (1/15)
= 10/30
= 1/3
They take 3 hours
Question 17

A

4

B

5

C

6

D

7

Part of tank filled by an inlet pipe in an hour = 1/6
Part of tank drained by an outlet pipe in an hour =1/8
If all the pipes are opened, the tank is drained in half a day (12 hours)
Part of tank drained in an hour when all are open = 1/12
Part of tank drained by (10x) outlet pipes – Part of tank filled by x inlet pipes = 1/12
[(10x) / 8] – [x/6] = 1/12
Solving,
3(10x)4x = 2
30 – 7x = 2
7x=28
X=4
There are 4 inlet pipes and 6 outlet pipes
Question 18

A

70 cans

B

14 cans

C

28 cans

D

84 cans

1 can is filled in 2 minutes
14 cans can be filled in 28 minutes
Question 19

A

12 hours

B

18 hours

C

1day

D

2 days

Part of tank emptied by the leak in an hour = 1/x
Part of tank filled in an hour = (1/8) + (1/12) – (1x)
=(5/24) – 1/x = 1/6
1/x = (5/24) –(1/6)
= 1/24
X= 24 hours
Question 20

A

2 hours

B

4 hours

C

4.5 hours

D

3 hours

Part of tank filled by pipe A in an hour = ¼
In the first hour, 1/4th of the tank is filled.
The remaining 3/4th of the tank is filled by A and B together
Part of tank filled by A and B in an hour = (1/4) +(1/8) = 3/8
Time taken to fill ¾ of the tank = (3/4) / (3/8) = 2 hours
The cistern is filled in 1+ 2 = 3 hours
Question 21

A

4.5 hours

B

6 hours

C

7.5 hours

D

) 7.5 hours

(1/y) = (1/3) – (1/5)
= 2/ 15
Y takes 15/2 = 7.5 hours to fill the tank
Question 22

A

360 liters

B

216 liters

C

180 liters

D

144 liters

= 180 * 1.2
= 216 liters
Question 23

A

1 hr 40 min

B

36 mins

C

20 mins

D

24 mins

=5/120
= 1/24
It takes 24 minutes to fill the tank
Question 24

A

12 hours

B

145 hours

C

18 hours

D

24 hours

Question 25

A

1 hour

B

36 min

C

45 min

D

54 min

Part of tank filled by pipe B in 1 minute = 1/90
Part of tank emptied by the outlet in 1 minute = 1/60
Part of tank filled when all the pipes are opened = part of tank filled by inletpart of tank emptied by outlet = (1/30) + (1/90) – (1/60)
= (6+23) / 180
= 1/ 36
The tank is filled in 36 mins
Question 26

A

70mins

B

(7/5)hrs

C

21(3/7)mins

D

42 mins

Full cistern is emptied in 30*7/5 = 42 minutes
Question 27

A

35 mins

B

30 mins

C

25 mins

D

20 mins

Part of cistern filled by A in 15 mins = 15/60 = ¼
Part of cistern filled by A and B in 1 minute = (1/60)+(1/30) = 1/20
¾ th of the cistern is filled by A and B
Time taken to fill ¾ of the cistern = (3/4) /(1/20) = 15 minutes
The cistern is filled in 30 minutes
Question 28

A

40 mins

B

1 hour

C

75 mins

D

90 mins

Part of tank filled by taps A in 1 minute = 1/120
(1/A) + (1/B) = (1/30)
(1/B) = (1/30) –(1/120) = (1/40)
B alone takes 40 mins to fill the tank
Question 29

A

22 minutes

B

15 minutes

C

11 minutes

D

6 minutes

Part of tank filled in the first 2 minutes = 2*1/6 = 1/3
2/3 of the tank is filled by X alone
Time taken by X to fill 2/3 of the tank = (2/3) / (1/33)
= 22 minutes
Question 30

A

20 hours

B

18 hours

C

24 hours

D

22.5 hours

Part of tank filled by B in 1 hour = 1/45
Part of tank filled by both in 1 hour = (1/36) + (1/45)
= 81 / (36*45)
= 1/20
They can fill the tank in 20 hours
Question 31

A

18

B

10

C

15

D

8

Question 32

A

18 hrs

B

36 hrs

C

35 hrs

D

9 hrs

They take 4 hours to fill the tank. But due to the leak, they take 4.5 hours to fill the tank
Part of tank emptied by leak in 1 hours = ¼  1/ 4.5
= ¼  2/9
= 1/36
The leak can empty the tank in 36 hours
Question 33

A

192 mins

B

144 mins

C

108 mins

D

81 mins

1/x + 1/3x = 1/36
4/3x = 1/36
X= 48
3x = 144
Question 34

A

30/17

B

30/11

C

9/2

D

60/17

= 17/60
The tank will be filled in (60/17 ) hours
Question 35

A

4 hrs

B

3hrs 45 mins

C

4 hrs 15 mins

D

3 hrs 15 mins

Now, 4 taps are filling the tank
Time taken by 1 tap to fill half the tank = 3
Time taken by 4 taps to fill half the tank = ¾
Total time taken = 3 hrs 45mins
Question 36

A

6.5 hrs

B

4.5 hrs

C

5 hrs

D

7.2 hrs

The cistern gets filled in 36/5 = 7.2 hours
Question 37

A

10 hrs

B

15 hrs

C

30 hrs

D

6 hrs

B = A 5
B = C + 4
C =A – 9
1/A + 1/(A5) = 1/(A9)
1/(A  9) – 1/(A5) = 1/A
Substitute the options given in the place of A
If A = 10,
1 – 1/5 not equal to 1/10
If A = 15,
1/6 – 1/10 = 1/15
So, A = 15
Question 38

A

1/11

B

5/11

C

6/11

D

8/11

= 3 * [(1/30)+(1/20)+(1/10)]
= 11/20
Part of tank filled by C in 3 minutes
= 3/10
Ratio = 3/10 : 11/20
= 6: 11
Question 39

A

17 minutes

B

12 minutes

C

19 minutes

D

21 minutes

1/x = 1/30 = 1/40 = 7/120
X= 120/7 = 17. 14 minutes
Question 40

A

16 mins

B

32 mins

C

48 mins

D

40 mins

1/x = 1/P – 1/Q
= 1/16 – 1/32
= 1/32
X= 32 mins
Question 41

A

8 hrs

B

6 hrs

C

2 hrs

D

1 hrs

B= A+6
We can check the options to find the answer
If A=8,
1/8 + 1/1 4 not equal to ¼
If A = 6,
1/6 + 1/12 = ¼
So, A = 6
Question 42

A

3.5

B

2

C

3

D

2.5

= (1/A) + (1/B) + (1/C)
=(1/5) + (1/10) + (1/30)
= 1/3
The tank will be filled in 3 hours
Question 43

A

8 hrs

B

14 hrs

C

7 hrs

D

13/3

½  1/x = 3/7
1/x = ½  3/7 = 1/14
X= 14
Question 44

A

6mins to fill

B

9 mins to fill

C

6 mins to empty

D

9 mins to empty

Part of tank emptied by B in 1 minute = 1/6
The rate at which pipe B empties is higher than the rate at which the pipe A fills the tank
Part of tank emptied in 1minute when A and B are opened = 1/6 – 1/10
= 1/ 15
Time taken to empty 2/5th of the tank
= 2/5 / 1/15
= 6 minutes
Question 45

A

10 mins

B

15 mins

C

12 mins

D

20 mins

= 1/15
Part of tank filled by both the taps in 10 minutes = 2/3
The remaining 1/3 of the tank is filled by the second tap alone.
Time taken to fill 1/3 of the tank = (1/3) /(1/60)
= 20 minutes
Question 46

A

8

B

15

C

16

D

18

= 162 litres
Number of 9 liters buckets needed = (162/9) = 18
Question 47

A

60 hrs

B

80 hrs

C

70 hrs

D

90 hrs

The leak will empty the cistern in 90 hrs
Question 48

A

5mins

B

12 mins

C

10 mins

D

15(2/3) mins

= 1/20 + 1/15 + 1/12
= 1/5
The cistern will be filled in 5 mins
Question 49

A

7mins 45 sec

B

8 mins 5 sec

C

7 mins 15 sec

D

8 mins 15 sec

= (1/A) + (1/B)
= 3/20
Part of the bucket filled by A and B in 3 minutes = 9/20
The remaining 11/20 of the bucket is filled by B alone
Time taken = (11/20) / (1/15)
= 33/4 minutes
= 8 mins 15 seconds
Question 50

A

7 hrs

B

7hrs 30 mins

C

8 hrs

D

8 hrs 30 mins

= 2/15
The tank will be filled in 15/2 hrs
= 7 hrs 30 minutes
Question 51

A

5 hrs

B

12.5 hrs

C

6 hrs

D

7.5 hrs

= 1/6
The tank will be filled in 6 hours
Question 52

A

5 hrs

B

7 hrs

C

6 hrs

D

8 hrs

Part of the cistern filled by the second tap in 1 hour = 1/3
Part of the cistern filled in 1 hour when both the taps are opened = (1/2) – (1/3)
= 1/6
The cistern will be filled in 6 hours
Question 53

A

8 minutes

B

12 minutes

C

10 minutes

D

16 minutes

= 1/10
The waste pipe takes 10 minutes to empty the cistern
Question 54

A

10 hrs 30 mins

B

21 hours

C

12 hours

D

24 hours

= 3.5 hours
= 7/2 hours
Work done by the leak in 1 hour
= (1/3) – (2/7)
= 1/21
The leak will empty the tank in 21 hours
Question 55

A

20 hrs

B

20 hrs

C

35 hrs

D

cannot be determined

Let the time taken by A to fill the tank be X hours
B is twice as fast as A
Time taken by B = x/2 minutes
C is twice as fast as B
Time taken by C = x/4 minutes
1/x + 2/x + 4/x = 1/5
X= 35
Question 56

A

10 mins 20sec

B

11mins 45 sec

C

12mins 30

D

15 mins

Part of tank filled by B in x minutes = x/40
Part of tank filled by A and B in 1 minute = 1/60 + 1/40
= 1/24
Part of tank filled by A and B in x minutes= x/24
x/40 + x/24 = 1
8x = 120
X = 15
The total time taken is 2x = 30 minutes
Question 57

A

15 mins

B

20 mins

C

27.5 mins

D

30 mins

Part of tank filled by B in x minutes = x/40
Part of tank filled by A and B in x minutes = x/40 + x/60
x/40 + x/40 +x/60 =1
x= 15
2x = 30
Question 58

A

10

B

12

C

14

D

16

The remaining 2/3 of the tank is filled by A and B in 7 hours
Part of tank filled by A and B in 1 hour = (2/3) / 7 = 2/21
1/C = 1/6 – 2/21
= 3/42
= 1/14
C alone can fill the tank in 14 hours
Question 59

A

4hrs 30 mins

B

5hrs

C

5 hrs 15 mins

D

5 hrs 30 mins

1/4th of the tank is filled by 3 pipes in ½ hours
Time taken by the pipe to fill ¾ of the tank = 6*3/4 = 9/2
Total time taken = ½ + 9/2 = 5 hours
Question 60

A

72 mins

B

80 mins

C

100 mins

D

90 mins

1/D = 1/36 – 1/60 = 1/90
D alone takes 90 minutes to fill the tank
Question 61

A

15

B

12

C

14

D

41

Remaining part = 11/3 = 2/3
(A+B)’s 1 hour work = 2/21
C’s 1 hour work = [(A+B+C)’s 1 hour work – (A+B)’s1 hour work]
= (1/6 – 2/21) = 1/14
C alone can fill the tank in 14 hours
Question 62

A

60 gallons

B

100 gallons

C

120 gallons

D

180 gallons

Volume of 1/40 part = 3 gallons
Volume of whole = 3 * 40 = 120 gallons
Question 63

A

3 ¼ min

B

5 ¼ min

C

8 ¼ min

D

9 ¼ min

X= 8 ¼
Question 64

A

5260 liters

B

5760 liters

C

5846 liters

D

6970 liters

X= 24 hrs
24 * 60 * 4 =5760
Question 65

A

4PM

B

5.30 PM

C

6PM

D

5 PM

2 to 3 = ¼ + 1/5 = 9/20
After 3AM = ¼ + 1/5 – ½ =  1/20
¼ + 9/20 = 14/20
1 hr 1/20
? 14/20
14 hours 5 PM
Question 66

A

5/11

B

6/11

C

7/11

D

8/11

Question 67

A

1 13/17 hours

B

2 8/11

C

3 9/17

D

4 1/2 1

5 6 12 60
The tank will be full in 60 hours i.e., 3 9 hours.
17 17
Question 68

A

4 1/3 Hours

B

7 hours

C

8 hours

D

14 hours

2 7 14
Leak will empty the tank in 14 hrs.
Question 69

A

5 min.

B

9 min.

C

10 min.

D

15 min.

Part filled by (A + B) in x min. + Part filled by A in (30 x) min. = 1.
x 2 + 1 + (30  x). 2 = 1
75 45 75
11x + (60 2x) = 1
225 75
11x + 180  6x = 225.
x = 9.
Question 70

A

6 hours

B

10 hours

C

15 hours

D

30 hours

Then, second and third pipes will take (x 5) and (x  9) hours respectively to fill the tank.
1 + 1 = 1
x (x  5) (x  9)
x  5 + x = 1
x(x  5) (x  9)
(2x  5)(x  9) = x(x  5)
x2  18x + 45 = 0
(x  15)(x  3) = 0
x = 15. [neglecting x = 3]
Question 71

A

81 min.

B

108 min.

C

144 min.

D

192 min.

Then, faster pipe will fill it in x minutes.
3
1 + 3 = 1
x x 36
4 = 1
x 36
x = 144 min.
Question 72

A

15 min

B

20 min

C

27.5 min

D

30 min

60 40 24
Suppose the tank is filled in x minutes.
Then, x 1 + 1 = 1
2 24 40
x x 1 = 1
2 15
x = 30 min.
Question 73

A

3 hrs 15 min

B

3 hrs 45 min

C

4 hrs

D

4 hrs 15 min

Part filled by the four taps in 1 hour = 4 x 1 = 2 .
6 3
Remaining part = 1  1 = 1 .
2 2
2 : 1 :: 1 : x
3 2
x = 1 x 1 x 3 = 3 hours i.e., 45 mins.
2 2 4
So, total time taken = 3 hrs. 45 mins.
Question 74

A

6 hours

B

6 2/3 hours

C

7 hours

D

7 1/2 houurs

d) 7 1 hours
2
Answer: Option C
Explanation:
(A + B)'s 1 hour's work = 1 + 1 = 9 = 3 .
12 15 60 20
(A + C)'s hour's work = 1 + 1 = 8 = 2 .
12 20 60 15
Part filled in 2 hrs = 3 + 2 = 17 .
20 15 60
Part filled in 6 hrs = 3 x 17 = 17 .
60 20
Remaining part = 1  17 = 3 .
20 20
Now, it is the turn of A and B and 3 part is filled by A and B in 1 hour.
20
Total time taken to fill the tank = (6 + 1) hrs = 7 hrs.
Question 75

A

10

B

12

C

14

D

16

6 3
Remaining part = 1  1 = 2 .
3 3
(A + B)'s 7 hour's work = 2
3
(A + B)'s 1 hour's work = 2
21
C's 1 hour's work = { (A + B + C)'s 1 hour's work }  { (A + B)'s 1 hour's work }
= 1  2 = 1
6 21 14
C alone can fill the tank in 14 hours.
Question 76

A

60 gallons

B

100 gallons

C

120 gallons

D

180 gallons

15 20 24
= 1  11
15 120
=  1 . [ve sign means emptying]
40
Volume of 1 part = 3 gallons.
40
Volume of whole = (3 x 40) gallons = 120 gallons.
Question 77

A

20 hours

B

25 hours

C

35 hours

D

Cannot be determined

E

None of these

Then, pipes B and C will take x and x hours respectively to fill the tank.
2 4
1 + 2 + 4 = 1
x x x 5
7 = 1
x 5
x = 35 hrs.
Question 78

A

1 hour

B

2 hours

C

6 hours

D

8 hours

Then, pipe B will fill it in (x + 6) hours.
1 + 1 = 1
x (x + 6) 4
x + 6 + x = 1
x(x + 6) 4
x2  2x  24 = 0
(x 6)(x + 4) = 0
x = 6. [neglecting the negative value of x]
Question 79

A

12 min

B

15 min

C

15 min

D

50 min

20
Part filled by B in 1 min = 1 .
30
Part filled by (A + B) in 1 min = 1 + 1 = 1 .
20 30 12
Both pipes can fill the tank in 12 minutes.
Question 80

A

10 min. 20 sec

B

11 min. 45 sec.

C

12 min. 30 sec.

D

14 min. 40 sec.

15 20 15
Remaining part = 1  7 = 8 .
15 15
Part filled by B in 1 minute = 1
20
1 : 8 :: 1 : x
20 15
x = 8 x 1 x 20 = 10 2 min = 10 min. 40 sec.
15 3
The tank will be full in (4 min. + 10 min. + 40 sec.) = 14 min. 40 sec.
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