High Level Questions On Pipes And Cistern For SBI PO

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high level questions on pipes and cistern for sbi po
high level questions on pipes and cistern for sbi po

High Level Questions On Pipes And Cistern For SBI PO

High Level Pipes And Cistern Questions for SBI PO Prelims and Mains exam. Download SBI PO High Level Pipes And Cistern questions on with solutions.

Download High Level Questions On Pipes And Cistern For SBI PO

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Question 1: A tank is fitted with two inlet pipes A and B and an outlet pipe C. Pipe A can fill the empty tank in 12 minutes. While pipe B alone can fill it in 18 minutes. Pipe C can empty the full tank in 11 1/4 minutes. If all three pipes are opened simultaneously, in what time will the empty tank be filled?

a) 16 minutes

b) 18 minutes

c) 20 minutes

d) 22 minutes

e) None of these

Question 2: Two pipes can fill a tank in 10 hours and 16 hours respectively. A third pipe can empty the tank in 32 hours. If all the three pipes are opened simultaneously then in how much time the tank will be full ? (in hours)

a) $7\frac{11}{21}$

b) $7\frac{13}{21}$

c) $8\frac{4}{21}$

d) $6\frac{5}{14}$

e) $8\frac{9}{14}$

Question 3: Pipe A can fill a tank in 8 hours while another pipe B can fill it in 16 hours. A third pipe C can empity the full tank in 32 hours. All three pipes are opened simutaneously. In what time will an empity tank be filled ?

a) 5.5 hours

b) 6 hours

c) 6.4 hours

d) 7 hours

e) 7.2 hours

Question 4: Two taps A and B fill a cistern of volume 432 liters in 24 minutes. If their efficiencies are in the ratio 4:5, find the number of minutes B alone takes to fill the cistern.

a) 43.2

b) 46.3

c) 24.68

d) 36.4

e) 35.81

Question 5: An inlet pipe can fill a tank in 12 minutes. An outlet pipe can empty the same tank in 20 minutes. Mohit starts the inlet pipe at 10 a.m. At 10:05, the outlet pipe is opened accidently by Mohit. He realizes his mistake 8 minutes later and turns off the outlet pipe. At what time will the tank be completely filled?

a) 10:15:30

b) 10:17:48

c) 10:19:20

d) 10:18:15

e) 10:16:12

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Instructions

In each of the following questions, two different quantities are defined. Compare the two quantities and choose the appropriate option as the answer.

Question 6: Quantity 1: Time taken to fill a tank when both, the inlet and the outlet pipe are connected. It is known that the inlet pipe can fill the tank in 1 minutes while the outlet pipe can empty the tank in 1.5 minutes.
Quantity 2: Time taken by a train running at 54 km/hr to overtake another train which is running at 36 km/hr. The length of both the trains is 500 m.

a) Quantity 1 > Quantity 2

b) Quantity 1 < Quantity 2

c) Quantity 1 $\geq $ Quantity 2

d) Quantity 1 $\leq $ Quantity 2

e) Quantity 1 = Quantity 2

Instructions

Calculate the quantity I and the quantity II on the basis of the given information then compare them and answer the following questions accordingly.

Question 7: Quantity I: Two pipes A and B can fill a tank in 16 hours and 20 hours individually. A drain pipe C can empty the tank in 24 hours. A and B are opened for 4 hours and then closed. Then Pipe C is opened. In how much time the tank will be emptied?
Quantity II: 12.6 min

a) Quantity I > Quantity II

b) Quantity I < Quantity II

c) Quantity I $\leq$ Quantity II

d) Quantity I $\geq$ Quantity II

e) Quantity I = Quantity II or The relationship between Quantity I and Quantity II can’t be determined

Instructions

Calculate the quantity I and the quantity II on the basis of the given information then compare them and answer the following questions accordingly.

Question 8: Quantity I: Two pipes P and Q can fill a tank in 20 min and 30 min respectively. A drainage pipe C can empty the tank in 60 min. If all three pipes are opened together, then in how much time will the tank be filled?
Quantity II: 18 minutes

a) Quantity I > Quantity II

b) Quantity I < Quantity II

c) Quantity I $\leq$ Quantity II

d) Quantity I $\geq$ Quantity II

e) Quantity I = Quantity II or The relationship between Quantity I and Quantity II can’t be determined

Instructions

In the following question, Quantity 1 and Quantity 2 are given. Calculate the values and compare them and then choose the option accordingly:

Question 9: A tank is connected to 5 pipes. 3 pipes fill the tank and 2 pipes empty the tank. All the pipes are connected to the bottom of the tank. All the pipes that fill the tank are of the same capacity and all the pipes that empty the tank are of the same capacity. If one pipe that fills the tank and one pipe that empties the tank is opened simultaneously in a half-full tank, the tank will get emptied in 6 hours.
Quantity 1:Time taken by 1 filling pipe to fill a tank that is already 75% full.
Quantity 2:Time taken by 2 emptying pipes to empty a half-full tank

a) Quantity 1 $>$ Quantity 2

b) Quantity 1 $<$ Quantity 2

c) Quantity 1 $\geq$ Quantity 2

d) Quantity 1 $\leq$ Quantity 2

e) Quantity 1 $=$ Quantity 2 or no relation can be established

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Instructions

In the following question, Quantity 1 and Quantity 2 are given. Calculate the values and compare them and then choose the option accordingly.

 

Question 10: There are three taps A, B and C connected to a tank. A and B are inlet pipes whereas C is an outlet pipe. When A and B are open, the empty tank gets filled in 10 hours. When B and C are open, the empty tank gets filled in 25 hours. When A and C are open, the empty tank gets filled in 50 hours.
Quantity 1: Time taken by A alone to fill the tank when it is empty.
Quantity 2: Time taken by C alone to empty the tank when it if full.

a) Quantity 1 $>$ Quantity 2

b) Quantity 1 $<$ Quantity 2

c) Quantity 1 $\geq$ Quantity 2

d) Quantity 1 $\leq$ Quantity 2

e) Quantity 1 $=$ Quantity 2 or no relation can be established

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Answers & Solutions:

1) Answer (C)

Part of the tank filled in 1 minute when all three pipes are opened

= $\frac{1}{12} + \frac{1}{18} – \frac{\frac{1}{45}}{4}$

= $\frac{1}{12} + \frac{1}{18} – \frac{4}{45}$

= $\frac{9}{180} = \frac{1}{20}$

=> Required time = 20 minutes

2) Answer (B)

Total quantity = 160 units
Speed pipe 1 = 16 $\frac{units}{hours}$

Speed pipe 2 = 10 $\frac{units}{hours}$

Speed pipe 3 = 5 $\frac{units}{hours}$

 

Time reqd = Total Units / [Speed (pipe 1 + pipe 2) – Speed Pipe 3]

Time = 160/21 = 7 $\frac{13}{21}$ hours

3) Answer (C)

Pipe A 1 hour work = 1/8

Pipe B 1 hour work = 1/16

Pipe C 1 hour work = – 1/32

Here negative sign shows that it is doing negative work

Now when all pipes are opened simultaneously then 1 hour combined work = 1/8 + 1/16 – 1/32

= 5/32

So time taken by all pipes to fill the tank = 32/5 hours = 6.4 hours

4) Answer (A)

Let the efficiencies of taps A and B be a and b respectively.
==> 432/(a+b) = 24 ==> a+b = 432/24 = 18
a:b = 4:5 ==> a = 8, b=10.
Efficiency of tap B = Volume of the tank/time taken
==> 10 = 432/t ==> t = 43.2 minutes.

5) Answer (B)

Let the volume of the tank be 60 litres.
So the inlet pipe fills 5 litres per minutes and outlet pipe empties 3 litres per minute. For the first 5 minutes only inlet pipe is operating. Hence, it will fill 25 litres. For the next 8 minutes, only 2 litres is being filled per minute. Hence, at 10:13, 41 litres water will be there in the tank. Now 19 litres can be filled by the inlet pipe in 4 minutes and 48 seconds. Thus, the tank will be completely filled at 10:17:48.

6) Answer (B)

Let the volume of the tank be 3 units. So inlet pipe fills 3 units and outlet pipe empties 2 units. Thus, the effectively 1 unit is being filled every minute. Hence, 3 minutes are required.

Relative speed of the faster train = 18 km/hr = 5 m/s
Distance to be covered = 1000 m.
Time required = 1000/5 = 200 second = 3 minutes 20 seconds.

7) Answer (A)

Quantity I:
Let the units of work done by pipes be 240 (LCM of 16,20,24)
Efficiency of Pipe A = 240/16 = 15
Efficiency of PIpe B = 240/20 = 12
Efficiency of Pipe C = 240/(-24) = -10 (Negative indicates draining)

Given that Pipes A and B are opened for 4 hours.
Pipes A and B can together fill 27 units in 1 hour.
Pipes A and B can together fill 108 units in 4 hours.
Remaining → 240-108 = 132 units
Pipe C can empty 132 units of tank in 132/10 = 13.2 min

Quantity II: 12.6 min

Hence, Quantity I > Quantity II

8) Answer (B)

Quantity I:
Let the total units be 120 (LCM of 20,30,60)
Efficiency of Pipe A = 120/20 = 6 units/min
Efficiency of Pipe B = 120/30 = 4 units/min
Efficiency of Pipe C = 120/(-60) = -2 units/min (Negative indicates Draining)

Then all three pipes can fill the tank in $\frac{120}{6+4-2} = \frac{120}{8} = 15 min$

Quantity II: 18 min
Hence, Quantity I < Quantity II

9) Answer (A)

It has been given that a pipe that fills the tank and a pipe that empties the tank, when opened simultaneously in a half-full tank, will empty the tank in 6 hours. Therefore, a completely full tank will be emptied in 12 hours when one filling pipe and one emptying pipe is opened.
We can infer that the capacity of an emptying pipe is greater than the capacity of a filling pipe.

Time taken by 2 emptying pipes to empty a half-full tank is equal to the time taken by 4 emptying pipes to empty a full tank.

Time taken by one filling pipe to fill a tank that is already 75% full is equal to the time taken by 4 filling pipes to fill an empty tank.

Therefore, we are comparing the time taken by 4 filling pipes to fill an empty tank and the time taken by 4 emptying pipes to empty a full tank. Also, we know that an emptying pipe is more efficient than a filling pipe. Quantity 1 is greater than quantity 2 and hence, option A is the right answer.

10) Answer (B)

Let the capacity of the tank be 50 units.
Let A’s efficiency be a, B’s efficiency be b and C’s efficiency be c.
A and B can fill the empty tank in 10 hours.
=> a + b = 5 ……..(i)
B and C can fill the empty tank in 25 hours.
=> b – c = 2……..(ii)
A and C can fill the empty tank in 50 hours.
=> a – c = 1 ……..(iii)
On adding (ii) and (iii), we get
a + b – 2c = 3
or, 5 – 2c = 3
or, c = 1
Therefore, a = 2 and b = 3
So, efficiency of A to fill the tank is more than efficiency of C to empty the tank.
Thus, Quantity 2 is greater than Quantity 1.
Hence, option B is the correct answer.

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