1. Ingeniería

Pipe&Cisternrelatedproblems
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:
1
part filled in 1 hour = .
x
฀ If a pipe can empty a tank in y hours, then:
1
part emptied in 1 hour = .
y
฀ 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, then
the net part filled in 1 hour =
1 1
- .
x 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 1
- .
y x
1
Math Practice:
1. Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes, and 10
minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C
discharge chemical solutions P,Q and R respectively. What is the proportion of the solution
R in the liquid in the tank after 3 minutes?
A.
5
11
B.
6
11
C.
7
11
D.
8
11
Answer & Explanation
Answer: Option B
Explanation:
Part filled by (A + B + C) in 3 minutes = 3
Part filled by C in 3 minutes =
Required ratio =
1
1
1
11
11
+
+
= 3x
= .
30 20 10
60
20
3
.
10
3
20
6
x
= .
10 11
11
2. Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours.
If all the three pipes are opened together, then the tank will be filled in:
A.
1
13
hours
17
B.
2
C.
3
9
hours
17
D.
1
4 hours
2
2
8
hours
11
Answer & Explanation
Answer: Option C
Explanation:
1 1 1
17
= .
+ 5 6 12
60
60
9
hours i.e., 3 hours.
The tank will be full in
17
17
Net part filled in 1 hour
3.
A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 hours to fill the
tank. The leak can drain all the water of the tank in:
A.
1
4 hours
3
B.
7 hours
C.
8 hours
D.
14 hours
Answer & Explanation
Answer: Option D
Explanation:
Work done by the leak in 1 hour =
1
1 3
= .
2 7
14
Leak will empty the tank in 14 hrs.
4.
Two pipes A and B can fill a cistern in 37 minutes and 45 minutes respectively. Both pipes
are opened. The cistern will be filled in just half an hour, if the B is turned off after:
A.
5 min.
B.
9 min.
C.
10 min.
D.
15 min.
Answer & Explanation
Answer: Option B
Explanation:
Let B be turned off after x minutes. Then,
3
Part filled by (A + B) in x min. + Part filled by A in (30 -x) min. = 1.
2
1
2
+
+ (30 - x).
=1
75 45
75
11x (60 -2x)
+
=1
225
75
x
11x + 180 - 6x = 225.
x = 9.
5. A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously
fill the tank in the same time during which the tank is filled by the third pipe alone. The second
pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The
time required by the first pipe is:
A.
6 hours
B.
10 hours
C.
15 hours
D.
30 hours
Answer & Explanation
Answer: Option C
Explanation:
Suppose, first pipe alone takes x hours to fill the tank .
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)
4
6. Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3
gallons per minute. All the three pipes working together can fill the tank in 15 minutes.
The capacity of the tank is:
A.
60 gallons
B.
100 gallons
C.
120 gallons
D.
180 gallons
Answer & Explanation
Answer: Option C
Explanation:
Work done by the waste pipe in 1 minute =
1
1
1
+
15
20 24
1
11
15 120
1
= - . [-ve sign means emptying]
40
1
part = 3 gallons.
Volume of
40
=
Volume of whole = (3 x 40) gallons = 120 gallons.
7. 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?
A.
20 hours
B.
25 hours
C.
35 hours
D.
Cannot be determined
E.
None of these
Answer & Explanation
Answer: Option C
Explanation:
5
Suppose pipe A alone takes x hours to fill the tank.
Then, pipes B and C will take
x
x
and hours respectively to fill the tank.
2
4
1 2 4 1
+ + =
x x
x 5
7 1
=
x 5
x = 35 hrs.
8. Two pipes A and 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?
A.
1 hour
B.
2 hours
C.
6 hours
D.
8 hours
Answer & Explanation
Answer: Option C
Explanation:
Let the cistern be filled by pipe A alone in x 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]
6
9. 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?
A.
12 min
B.
15 min
C.
25 min
D.
50 min
Answer & Explanation
Answer: Option A
Explanation:
1
.
20
1
Part filled by B in 1 min = .
30
Part filled by A in 1 min =
Part filled by (A + B) in 1 min =
1
1
1
+
= .
20 30
12
Both pipes can fill the tank in 12 minutes.
10. Two pipes A and B can fill a tank in 15 minutes and 20 minutes respectively. Both the
pipes are opened together but after 4 minutes, pipe A is turned off. What is the total time
required to fill the tank?
A.
10 min. 20 sec.
B.
11 min. 45 sec.
C.
12 min. 30 sec.
D.
14 min. 40 sec.
Answer & Explanation
Answer: Option D
Explanation:
1
1
7
+
= .
15 20
15
7
8
= .
Remaining part = 1 15
15
1
Part filled by B in 1 minute =
20
1 : 8 :: 1 : x
Part filled in 4 minutes = 4
7
20
15
2
8
x=
x 1 x 20 = 10 min = 10 min. 40 sec.
15
3
The tank will be full in (4 min. + 10 min. + 40 sec.) = 14 min. 40 sec.
11. 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:
A.
81 min.
B.
108 min.
C.
144 min.
D.
192 min.
Answer & Explanation
Answer: Option C
Explanation:
Let the slower pipe alone fill the tank in x minutes.
Then, faster pipe will fill it in
x
minutes.
3
1
1 3
+ =
x x 36
4
1
=
x 36
x = 144 min.
12. A large tanker can be filled by two pipes A and B in 60 minutes and 40 minutes
respectively. How many minutes will it take to fill the tanker from empty state if B is used
for half the time and A and B fill it together for the other half?
A.
15 min
B.
20 min
C.
27.5 min
D.
30 min
Answer & Explanation
8
Answer: Option D
Explanation:
Part filled by (A + B) in 1 minute =
1
1
1
+
= .
60 40
24
Suppose the tank is filled in x minutes.
x 1
1
+
=1
2 24 40
1
x
x
=1
2 15
Then,
x = 30 min.
13. 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?
A.
3 hrs 15 min
B.
3 hrs 45 min
C.
4 hrs
D.
4 hrs 15 min
Answer & Explanation
Answer: Option B
Explanation:
Time taken by one tap to fill half of the tank = 3 hrs.
Part filled by the four taps in 1 hour = 4 x
Remaining part = 1 -
1
2
= .
6
3
1
1
= .
2
2
2 1
: :: 1 : x
3 2
1
3
3
x=
x1x
= hours i.e., 45 mins.
2
2
4
9
So, total time taken = 3 hrs. 45 mins.
14. 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 alternately, the tank will be full in:
A.
6 hours
B.
2
6 hours
3
C.
7 hours
D.
1
7 hours
2
Answer & Explanation
Answer: Option C
Explanation:
1
1
9
3
+
=
= .
12 15
60 20
1
8
2
1
+
=
= .
(A + C)'s hour's work =
12 20
60 15
3
2
17
+
= .
Part filled in 2 hrs =
20 15
60
17
17
= .
Part filled in 6 hrs = 3 x
60
20
17
3
= .
Remaining part = 1 20
20
3
Now, it is the turn of A and B and
part is filled by A and B in 1 hour.
20
(A + B)'s 1 hour's work =
Total time taken to fill the tank = (6 + 1) hrs = 7 hrs.
15. Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours,
C is closed and A and B can fill the remaining part in 7 hours. The number of hours taken
by C alone to fill the tank is:
A.
10
B.
12
C.
14
D.
16
Answer & Explanation
10
Answer: Option C
Explanation:
2 1
=
6 3
1
2
Remaining part = 1 = .
3
3
2
(A + B)'s 7 hour's work =
3
2
(A + B)'s 1 hour's work =
21
Part filled in 2 hours =
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.
16. To fill a cistern, pipes A, B and C take 20 minutes, 15 minutes and 12 minutes
respectively. The time in minutes that the three pipes together will take to fill the cistern, is
:
5
12
10
15 and 2/3
Answer & Explanation
5
Answer:
Explanation: Part filled by (A +B+ c) in 1 min. = (1/20) +(1/15) + (1/12) = 12/60 = 1/5
All the three pipes together will fill the tank in 5 min.
17. A tank can be filled by a tap in 20 minutes and by another tap in 6O minutes. Both the
taps are kept open for 10 minutes and then the first tap is shut off. After this, the tank will
be completely filled in:
10 miii.
15 mm.
11
12 mm.
20 mm.
Answer & Explanation
20 mm.
Answer:
Explanation: Part filled in 10 min = 10[(1/20) + (1/60)] = 10 * (4/60) = 2/3
Remaining part = (1 - (2/3)) = 1/3
Part filled by second tap in 1 min = 1/60
(1/60) : (1/3) ∷ 1 : x
Hence, the remaining part will be filled in 20 min.
18. Two pipes A and B can fill a cistern in 12 minutes and 16 minutes respectively. If both
the pipes are opened together, then after how much time B should be closed so that the tank
is full in 9 minutes ?
3 min and 30 sec.
4 min and 30 sec.
4 min.
4 min 77 sec.
Answer & Explanation
4 min.
Answer:
Explanation: Let B be closed after x minutes. Then,
Part filled by (A + B) in x min. + Part filled by A in (9 — x) min, = 1
x[(1/12) + (1/16)] + (9 - x)(1/12) = 1 or (7x/48) + (9-x)/12 = 1
or7x + 36 — 4x = 48 or x=4.
So, B must be closed after 4 minutes.
19. A tap can fill a tank in 16 minutes and another can empty it in8 minutes. If the tank is
already half full and both the tanks are oped together, the tank will be:
filled in 12 mm.
filled in 8 mm,
emptied in 12 mm.
emptied in 8 mm.
Answer & Explanation
emptied in 8 mm.
Answer:
Explanation: Rate of waste pipe being more, the tank will be emptied when both the
pipes are opened.
Net emptying work done by both in 1 min = (1/8) - (1/16) = 1/16
Now, full tank will be emptied by them in 16 min.
Half full tank will be emptied in 8 min.
20. An electric pump can fill a tank in 3 hours. Because of a leak in the tank, it took 3
hours 30 min to fill the tank. The leak can drain out all the water of the tank in :
12
10 hours 30 min
21 hours
12 hours
24 hours
Answer & Explanation
21 hours
Answer:
Explanation: Work done by the leak in 1 hour = (1/3) - (2/7) = 1/21 .
Leak will mpty the tank in 21 hours.
21. 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 litres a minute. When the tank is full, the inlet is opened and due to the leak
the tank is empty in 8 hours. The capacity of the tank (in litres) is
5260
5846
5760
6970
Answer & Explanation
5760
Answer:
Explanation: Work done by the inlet in 1 hour = (1/6) - (1/8) = 1/24
Work done by the inlet in 1 min = (1/24) * (1/60) = 1/1440
Volume of 1/1440 part = 4 liters.
Volume of whole = (1440 * 4) litres = 5760 litres.
22. Taps A and B can fill a bucket in 12 minutes and 15 minutes respectively. If both are
opened and A is closed after 3 minutes, how much further time would it take for B to fill the
bucket?
7 nun. 45 sec.
8 mm. 5 sec.
7 mm. 15 sec.
8 mm. 15 sec.
Answer & Explanation
8 mm. 15 sec.
Answer:
Explanation: Part filled in 3min = 3[(1/12) + (1/15)] = 3 * (9/60) = 9/20
Remaining part = 1 - (9/20) = 11/20
Part filled by B in 1 min = 1/15
(1/15) : (11/20) = 1 : x or x = (11/20) * 1 * (15/1) = 8 min 15 sec
Remaining part is filled by B in 8 ruin. 15 sec.
23. 12 buckets of water fill a tank when the capacity of each bucket is 13.5 litres. How many
buckets will be needed to fill the same tank, if the capacity of each bucket is 9 litres?
8
15
13
16
18
Answer & Explanation
18
Answer:
Explanation: Capacity of the tank = (12 * 13.5) litres = 162 litres.
Capacity of each bucket = 9 litres
Number of buckets needed = (162/9) = 18.
24. 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?
7580
8290
7960
8640
Answer & Explanation
8640
Answer:
Explanation: Work done by the inlet in 1 hour = (1/8) - (1/12) = 1/24
Work done by the inlet in 1 min = (1/24) * (1/60) = 1/1440
Volume of 1/1440 part = 6 litres
Volume of whole = (1440 x 6) litres 8640 litres.
25. A cistern can be filled in 9 hours but it takes 10 hours due to in its bottom. If the cistern
is full, then the time that the leak will take to empty it, is:
60 hrs
80 hrs
70 hrs
90 hrs
Answer & Explanation
90 hrs
Answer:
Explanation: Work done by the leak in 1 hour = (1/9 - 1/10) = 1/90.
Leak will empty the full cistern in 90 hrs
26. 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 litres a minute. When the tank is full, the inlet is opened
and due to the leak the tank is empty in 8 hours. The capacity of the tank (in litres) is
5260
5846
5760
6970
Answer & Explanation
14
5760
Answer:
Explanation: Work done by the inlet in 1 hour = (1/6) - (1/8) = 1/24
Work done by the inlet in 1 min = (1/24) * (1/60) = 1/1440
Volume of 1/1440 part = 4 liters.
Volume of whole = (1440 * 4) litres = 5760 litres.
27. A tank can be filled by a tap in 20 minutes and by another tap in 6O minutes.
Both the taps are kept open for 10 minutes and then the first tap is shut off. After
this, the tank will be completely filled in:
10 miii.
15 mm.
12 mm.
20 mm.
Answer & Explanation
20 mm.
Answer:
Explanation: Part filled in 10 min = 10[(1/20) + (1/60)] = 10 * (4/60) = 2/3
Remaining part = (1 - (2/3)) = 1/3
Part filled by second tap in 1 min = 1/60
(1/60) : (1/3) ∷ 1 : x
Hence, the remaining part will be filled in 20 min.
28. 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?
7580
8290
7960
8640
Answer & Explanation
8640
Answer:
Explanation: Work done by the inlet in 1 hour = (1/8) - (1/12) = 1/24
Work done by the inlet in 1 min = (1/24) * (1/60) = 1/1440
Volume of 1/1440 part = 6 litres
Volume of whole = (1440 x 6) litres 8640 litres.
29. To fill a cistern, pipes A, B and C take 20 minutes, 15 minutes and 12 minutes
respectively. The time in minutes that the three pipes together will take to fill the
cistern, is :
5
12
10
15 and 2/3
15
Answer & Explanation
5
Answer:
Explanation: Part filled by (A +B+ c) in 1 min. = (1/20) +(1/15) + (1/12) = 12/60 = 1/5
All the three pipes together will fill the tank in 5 min.
30. Two taps A and B can fill a tank in 10 hours and 15 hours respectively. If both
the taps are opened together, the tank will be full in:
5 hrs
12 and 1/2 hrs
6 hrs
7 and 1/2 hrs
Answer & Explanation
6 hrs
Answer:
Explanation: As hours work=1/10, Bs 1 hours work = 1/15,
(A+B)s 1 hours work = (1/10) + (1/15) = 5/30 = 1/6
Both the taps can fill the tank in 6 hours.
31. Pipe A fills a tank in 30 minutes. Pipe B can fill the same tank 5 times as fast as pipe A. If
both the pipes were kept open when the tank is empty, how much time will it take for the tank to
overflow?
Explanatory Answer
Pipe B fills the tank 5 times as fast as pipe A.
Therefore, pipe B will fill the tank in one-fifth of the time that pipe A takes.
Pipe B will fill the tank in
In 1 minute, pipe A will fill
= 6 minutes.
th of the tank and pipe B will fill
th of the tank.
Therefore, together, the two pipes will fill
th of the tank in a minute
Hence, the two pipes working together will take 5 minutes to fill the tank.
32. Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes,
16
and 10 minutes respectively. When the tank is empty, all the three pipes are opened.
A, B and C discharge chemical solutions P, Q and R respectively. What is the
proportion of the solution R in the liquid in the tank after 3 minutes?
Answer:
A takes 30 minutes to fill 1 part
A takes 1 minute to fill 1/30 part
B takes 20 minutes to fill 1 part
B takes 1 minute to fill 1/20 part
C takes 10 minutes to fill 1 part
C takes 1 minute to fill 1/10 part
so, in 1 minute A+B+C fill (1/30+1/20+1/10)
= 11/60
so, in 3 minutes A+B+C fill (3*11)/60
= 11/20
in 3 minutes C fills = (1*3)/10
= 3/10
so, proportion of R = (3/10)/(11/20)
= 6/11
Ans. 6/11.
33. Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12
hours. If all the three pipes are opened together, then the tank will be filled in:
Answer:
A takes 5 hours to fill 1 part
17
A takes 1 hour to fill 1/5 part
B takes 6 hours to fill 1 part
B takes 1 hour to fill 1/6 part
C takes 12 hours to empty 1 part
C takes 1 hour to empty 1/12 part
so, in 1 hour A+B+C fill (1/5+1/6-1/ 12)
= (12+10-5)/60
= 17/60 part
17/60 part is filled in 1 hour
so, 1 part is filled in (1*60)/17 hour
= 3 hours 31 minutes 46 seconds
34. Two pipes can fill a tank in 24 and 28 minutes respectively and a waste pipe can
empty 3 gallons per minute. All the three pipes working together can fill the tank in
15 minutes. The capacity of the tank is:
Answer:
Let, capacity of tank is x
First pipe takes 24 minutes to fill x
First pipe takes 1 minute to fill x/24
Second pipe takes 28 minutes to fill x Second pipe takes 1 minute to fill x/28
According to question, 15(x/24 + x/28 -3)=x >(7x +6x-504)/168=x/15
>13x-504=56x/5
>65x-2520=56x
>9x=2520
>x=280
18
Capacity of the tank is 280 gallons
Ans. 280 gallons.
35. A large tanker can be filled by two pipes A and B in 6 minutes and 4 minutes
respectively. How many minutes will it take to fill the tanker from empty state if B is
used for half the time and A and B fill it together for the other half?
Answer:
Let, total time is x
Pipe A takes 6 mins to fill 1 part
Pipe A takes 1 min to fill 1/6 part
Pipe B takes 4 mins to fill 1 part
Pipe B takes 1 mins to fill 1/5 part
According to question,
{(1/6 )* (x/2)}+ {(1/4)* x} = 1
>(x/12)+(x/4) = 1
>(x+3x)/12=1
>4x=12
>x=3
36. Three pipes A, B and C can fill a tank in 60 hours. After working at it together for 20
hours, C is closed and A and B can fill the remaining part in 70 hours. The number of
hours taken by C alone to fill the tank is:
Answer:
Pipes A, B and C take 60 hours to fill 1 part
Pipes A, B and C take 1 hours to fill 1/60 part
19
Pipes A, B and C take 20 hours to fill (1*20)/60 part
=1/3 part
Remaining part = 1-(1/3) = 2/3
In 70 hours A & B fills 2/3 part
In 1 hour A & B fills 2/ (70*3) part
In 60 hours A & B fills (2*60)/(3*70) part
= 4/7 part
Remaining part = 1-(4/7) = 3/7
C fills 3/7 part in 60 hours
C fills 1 part in (60*7)/3 hours
= 140 hours
Ans. 140 hours.
37. A tank is filled in 5 hours by three pipes A, B and C. The pipe C is 3times as fast as B
and B is 3times as fast as A. How much time will pipe A alone take to fill the tank?
Answer:
Let, C can fill a tank in x hours
so, A can fill in 9x hours &
B can fill in 3x hours
According to question,
(5/9x)+(5/3x)+(5/x) = 1
>(5+15+45)/9x = 1
>9x=65
>x=65/9
20
so, A can fill the tank
= 9* (65/9)
= 65
Ans. 65 hours.
38. A tank can be filled by two taps A and B in 8 hoursand 10 hours respectively. The full
tank can be emptied by a third tap C in 9 hours. Ifall the taps are turned on at the
same time, in how much time will the empty tank be filled up completely?
Answer:
A takes 8 hours to fill 1 part
A takes 1 hour to fill 1/8 part
B takes 10 hours to fill 1 part
B takes 1 hour to fill 1/10 part
C takes 9 hours to empty 1 part
C takes 1 hour to empty 1/9 part
so, in 1 hour A+B+C fill (1/8+1/10-1/9)
= (45+36-40)/360
= 41/360 part
41/360 part is filled in 1 hour
so, 1 part is filled in (1*360)/41 hour
= 8 hours 46 minutes 50 seconds
Ans. 8h 46 mins 50 secs
39. A cistern can be filled by two taps A and B in 6hours and 8 hours respectively. The
full cistern can be emptied by a third tap C in 4 hours. If all the taps are turned on at
21
the same time, in how much time will the empty cistern be filled completely?
Answer:
A takes 6 hours to fill 1 part
A takes 1 hour to fill 1/6 part
B takes 8 hours to fill 1 part
B takes 1 hour to fill 1/8 part
C takes 4 hours to empty 1 part
C takes 1 hour to empty 1/4 part
so, in 1 hour A+B+C fill (1/6+1/8-1/4)
= (4+3-6)/24
= 1/24 part
1/24 part is filled in 1 hour
so, 1 part is filled in (1*24)/1 hour
= 24 hours
Ans. 24 hours
40. 12 buckets of water fill a tank when the capacity of each bucket is 13.5 litres. How
many buckets will be needed to fill the same tank, if the capacity of each bucket is 9
litres? .
Answer:
capacity of each bucket is 13.5 litres
12 buckets are needed to fill the tank
so, capacity of the tank = 12*13.5
= 162 liters
if the capacity of each bucket is 9 litres Required number of bucket
22
= 162/9
= 18
Ans. 18 buckets
41. 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 litres a minute. When the tank is full, the inlet is opened and
due to the leak the tank is empty in 8 hours. The capacity of the tank (in litres) is
Answer:
In 6 hours a leak can empty 1 part
In 1 hour a leak can empty 1/6 part
In 8 hours a pipe can empty 1 part
In 1 hour a pipe can empty 1/8 part
so, In 1 hours the tank is filled by (1/6)-(1/8) part
= 1/24 part
1/24 part can be filled in 1 hour
1 part can be filled in (1*24)/1 hour
= 24 hours
In 1 minute the pipe fills 4 litters
so, In (24*60)= 1440 minutes the pipe fills (4*1440) = 5760 litters
Ans. 5760 litters.
42. One tap can fill a cistern in 2 hours and another tap can empty the cistern in 3 hours.
How long will they take to fill the cistern if both the taps are opened ?
Answer:
In 2 hours one tap can fill 1 part
23
In 1 hours one tap can fill 1/2 part
In 3 hours one tap can empty 1 part
In 1 hours one tap can empty 1/3 part
So, In 1 hour the two tap can fill (1/2)-(1/3) part
= (3-2)/6 part
= 1/6 part
1/6 part can be filled in 1 hour
so, 1 part can be filled (1*6)/1 hour
= 6 hours
Ans. 6 hours.
43. A cistern can be filled in 9 hours but it takes 10 hours due to a leak in its bottom. If
the cistern full, then the time the tank leak will take to empty it is :
Answer:
In 9 hours the tank is filled by 1 part
In 1 hour the tank can be filled 1/9 part
In 10 hours the tank can be emptied by 1 part
In 1 hour the tank can be emptied 1/10 part
So, In 1 hour the tank can be emptied by (1/9)- (1/10) part
= (10-9)/90 part
= 1/90 part
1/90 part can be emptied in 1 hour
so, 1 part can be emptied in (1*90)/1 hour
= 90 hours
24
Ans. 90 hours.
25