Pipes and Cisterns Questions for RRB NTPC PDF

Pipes and Cisterns Questions for RRB NTPC PDF

Download RRB NTPC Pipes and Cisterns Questions and Answers PDF. Top 16 RRB NTPC Pipes and Cisterns questions based on asked questions in previous exam papers very important for the Railway NTPC exam.

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Question 1: Three pipes are made of different shapes. The cross-sections of the pipes are an equilateral triangle, a hexagon and a circle. The perimeter of each of these cross-sections is equal. The flow through the pipes is proportional to the area of cross section. If it takes 8 minutes for the triangular pipe to fill up the tank, what will be the difference in the times taken by the hexagonal and circular pipes?

a) 45 seconds

b) 1 minute

c) 0.5 minutes

d) 7.9 minutes

Question 2: Two taps can separately fill a cistern in 10 minutes and 15 minutes respectively. If these two pipes and a waste pipe are kept open simultaneously, the cistern gets filled in 18 minutes. The waste pipe can empty the full cistern in

a) 7 minutes

b) 13 minutes

c) 23 minutes

d) 9 minutes

Question 3: A, B and C are three pipes attached to a cistern. A and B can fill it in 20 minutes and 30 minutes respectively, while C can empty it in 15 minutes. If A, B and C be kept open successively for 1 minute each, how soon will the cistern be filled?

a) 180 minutes

b) 60 minutes

c) 157 minutes

d) 155 minutes

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Question 4: A bath can be filled by the cold water and hot water pipes in 10 minutes and 15 minutes respectively. A person leaves the bathroom after turning on both pipes simultaneously and returns at the moment when the bath should be full. Finding, however, that the waste pipe has been open, he then closes it. In exactly four minutes more the bath is full. In how much time would the waste pipe empty the full bath, if it alone is opened?

a) 9 minutes

b) 10 minutes

c) 12 minutes

d) None of these

Question 5: To fill a certain tank, pipes A, B and C take 20 minutes, 15 minutes and 12 minutes respectively. If the three pipes are opened every alternate minute, how long will it take to fill the tank?

a) 5 minutes

b) 10 minutes

c) 12 minutes

d) 15 minutes

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 6: 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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Question 7: A cistern is connected to 10 pipes. Some pipes fill the tank while the rest empty the tank. The capacity of each pipe is the same (both filling and emptying pipes). If all the pipes that fill the tank are opened and all the pipes that empty the tank are closed, an empty tank will be full in 20 minutes. If all the pipes that empty the tank are opened and all the pipes that fill the tank are closed, a half-full tank will be emptied in 15 minutes. If all the pipes that fill the tank and half the pipes that empty the tank are opened in an empty tank, the time in which the tank will be filled (in minutes) is

Question 8: Pipe A can fill a tank in 12 hours and pipe B can fill the tank in 18 hours. If both the pipes are opened on alternate hours and if pipe B is opened first, then in how much time (in hours) the tank will be full?

a) $14\frac{1}{3}$

b) $14\frac{2}{3}$

c) $14\frac{1}{2}$

d) $14\frac{2}{5}$

Question 9: Two pipes can independently fill a bucket in 20 minutes and 25 minutes. Both are turned on together for 5 minutes after which the second pipe is turned off. What is the time taken by the first pipe alone to fill the remaining portion of the bucket ?

a) 11 minutes

b) 16 minutes

c) 20 minutes

d) 15 minutes

Question 10: A pipe can fill a cistern in 12 minutes while a second pipe fills it in 15 minutes. But a third pipe can empty that completely filled cistern 16 minutes. The first two pipes are kept open for 5 minutes initially and then the third one is also opened. Then the further time (in minutes) taken to empty that cistern is

a) 30

b) 40

c) 45

d) 50

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Question 11: Two pipes can separately fill a tank in 20 hrs and 30 hrs respectively. Both these pipes are opened simultaneously and after the tank is $\ \frac{1}{3}$rd full, a leak develops in the tank through which $\frac{1}{3}$rd of water supplied thereafter by both pipes gets leaked out. The total time (in hours) taken to fill the tank is

a) 18

b) 16

c) 15

d) 12

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 12: 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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Question 13: A tank is fitted with pipes, some filling it and the rest draining it. All filling pipes fill at the same rate, and all draining pipes drain at the same rate. The empty tank gets completely filled in 6 hours when 6 filling and 5 draining pipes are on, but this time becomes 60 hours when 5 filling and 6 draining pipes are on. In how many hours will the empty tank get completely filled when one draining and two filling pipes are on?

Question 14: A tank is connected to a certain number of pipes. Few of these pipes fill the tank and the remaining pipes empty the tank. If all the pipes are opened, an empty tank will get filled in 20 minutes. If the pipes that empty the tank are closed, then an empty tank will be filled in 12 minutes. How much time will all the outlet pipes take to empty a completely filled tank?

a) 20 minutes

b) 30 minutes

c) 40 minutes

d) 60 minutes

Question 15: 4 identical pipes, when opened simultaneously, can fill a cistern in 20 minutes. How many minutes it will take 2 such pipes to fill the empty cistern to 60% mark when opened simultaneously?

a) 24 minutes

b) 20 minutes

c) 16 minutes

d) 25 minutes

e) 30 minutes

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Answers & Solutions:

1) Answer (C)

Let the sides of triangle be a, that of hexagon be b and circle be c.

Given:

3a = 6b = 2πr

Given: flow rate is proportional to area, so, Flow rate(F) = k Area

Area of triangle = √3/4 a^2

Area of hexagon = 3√3/8 a^2

Area of circle = πr^2 = 9a^2/4π

If triangular pipe takes 480 seconds, hexagonal and circular pipe will take 320 and 290 seconds.

Required difference = 30 seconds = 0.5 minutes.

2) Answer (D)

Let, the time taken by waste pipe to empty the cistern = ‘$x$’

Part filled by two pipes in 1 minute is 1/10 and 1/15 respectively and the cistern gets filled in 18 minutes (given).

Net part filled in 1 hour is given by,

$\frac{1}{10} + \frac{1}{15} – \frac{1}{x} = \frac{1}{18}$

$\frac{1}{10} + \frac{1}{15} – \frac{1}{18} = \frac{1}{x}$

$\frac{9 + 6 – 5}{90} = \frac{1}{x}$

$\frac{10}{90} = \frac{1}{x}$ or $x = 9$ minutes

Hence, option D is the correct answer.

3) Answer (A)

Part filled by A, B and emptied by C in one minute = $\frac{1}{20}, \frac{1}{30}$ and $\frac{1}{15}$

Part filled by three pipes in 3 minutes = $\frac{1}{20} + \frac{1}{30}$ – $\frac{1}{15}$

$\Rightarrow \frac{3 + 2 – 4}{60} = \frac{1}{60}$

Cistern can be filled in 60 x 3 = 180 minutes.

Hence, option A is the correct answer.

4) Answer (D)

Time taken by the hot and cold water pipes to fill the bath,

= $\frac{10 \times 15}{10 + 15} = 6$ min

Total time taken to fill the bath including the empty pipe is also open = (6 + 4) = 10 min

Let ‘$x$’ be the time taken by empty pipe to empty the bath.

$\therefore \frac{1}{10} + \frac{1}{15} + \frac{1}{x} = \frac{1}{10}$

$\Rightarrow \frac{1}{x} = \frac{1}{15}$

$\Rightarrow x = 15$ min

Hence, option D is the correct answer.

5) Answer (D)

Part filled by 3 pipes in 3 minutes = $\frac{1}{20} + \frac{1}{15} + \frac{1}{12} = \frac{3 + 4 + 5}{60} = \frac{1}{5}$

1/5th of the tank is filled in 3 minutes then whole tank is filled in 5 x 3 = 15min

Hence, option D is the correct answer.

6) 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.

7) Answer: 30

Let the number of pipes that fill the tank be x.
=> Number of pipes that empty the tank = 10-x.
Let us assume the capacity of each pipe to be 1 unit/minute.

The tank will be full in 20 minutes if all the pipes that fill the tank are opened and all the pipes that empty the tank are closed.
=> Capacity of the tank = 20*x —–(1)

If all the pipes that empty the tank are opened and all the pipes that fill the tank are closed, a half-full tank will be emptied in 15 minutes. Therefore, a full tank will be emptied in 30 minutes if all the tanks that empty the tank are opened and all the tanks that fill the tank are closed.

=> Capacity of the tank = 30*(10-x) —–(2)

Equating (1) and (2),
20x = 300 – 30x
50x = 300
x = 6

The number of pipes that fill the tank is 6 and the number of pipes that empty the tank is 4.
If all the pipes that fill the tank and half the pipes that empty the tank are opened, then 6-2 = 4 pipes will be filling the tank.

Capacity of the tank is 20x = 20*6 = 120 units.
=> Time taken = 120/4 = 30 minutes.

Therefore, 30 is the right answer.

8) Answer (C)

Let capacity of tank = L.C.M. (12,18) = 36 litres

Pipe A can fill a tank in 12 hours, => Pipe A’s efficiency = $\frac{36}{12}=3$ litres/hr

Similarly, pipe B’s efficiency = $\frac{36}{18}=2$ litres/hr

Now, in 2 hours tank filled is (B opened first) = $2+3=5$ litres

$\because$ $5\times7=35$, hence 35 litres of tank is filled in 14 hours.

Now, B is opened and it will fill the remaining 1 litre in $\frac{1}{2}$ hour.

$\therefore$ Total time taken = $14\frac{1}{2}$ hours

=> Ans – (C)

9) Answer (A)

Let capacity of bucket = L.C.M. (20,25) = 100 litres

First pipe can fill it in 20 minutes, => first pipe’s efficiency = $\frac{100}{20}=5$ l/min

Similarly, second pipe’s efficiency = $\frac{100}{25}=4$ l/min

=> Volume of bucket filled by both in five minutes = $(5+4)\times5=45$ litres

$\therefore$ Time taken by the first pipe alone to fill the remaining portion of the bucket = $\frac{(100-45)}{5}=11$ minutes

=> Ans – (A)

10) Answer (C)

11) Answer (B)

12) 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.

13) Answer: 10

Let the efficiency of filling pipes be ‘x’ and the efficiency of draining pipes be ‘-y’.
In the first case,
Capacity of tank = (6x – 5y) * 6……….(i)
In the second case,
Capacity of tank = (5x – 6y) * 60…..(ii)
On equating (i) and (ii), we get
(6x – 5y) * 6 =  (5x – 6y) * 60
or, 6x – 5y = 50x – 60y
or, 44x = 55y
or, 4x = 5y
or, x = 1.25y

Capacity of the tank = (6x – 5y) * 6 = (7.5y – 5y) * 6 = 15y
Net efficiency of 2 filling and 1 draining pipes = (2x – y) = (2.5y – y) = 1.5y
Time required = $\dfrac{\text{15y}}{\text{1.5y}}$hours = 10 hours.

Hence, 10 is the correct answer.

14) Answer (B)

Let the capacity of the tank be 120 litres.
If all the pipes are open, the tank will be filled in 20 minutes.
=> The net inflow = 120/20 = 6 litres per minute.
If the pipes that empty the tank are closed, then the tank gets filled in 12 minutes.
=> Net capacity of the inlet pipes = 120/12 = 10 litres/minute.
Capacity of the outlet pipes = 4 litres per minute.
The outlet pipes will take 120/4 = 30 minutes to empty a completely full tank. Therefore, option B is the right answer.

15) Answer (A)

Let ‘x’ be the quantity of water pumped in by one pipe in one minute.
Hence, the volume of the cistern = 20*4*x = 80x
The cistern is empty and needs to be filled to 60% mark. Hence, the volume of the water that is needed to be pumped = 0.60*80x = 48x
Therefore, the time taken by 2 pipes to fill the cistern to 60% mark = $\dfrac{48x}{2x}$ = 24 minutes.
Hence, option A is the correct answer.

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