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QUESTION: 1

A Tank is filled with the mixture of Milk and Water in the ratio of 3:2 up to 2/5 of its capacity. The tank has two inlet pipes i.e., Milk and Water inlets. Milk and Water pipe can fill an empty tank in 12 and 18 hours respectively. Now both pipes are opened simultaneously and closed after the Tank is completely filled, then what is the ratio of Milk and Water in the full Tank if it can accommodate 250Litre?

Solution:

Initial Milk = 2/5*250*3/5 = 60 L

Water = 2/5*250*2/5 = 40 L

Rest of Tank =150 L

Pipes are opened then can fill rest of tank in 108/25 hours

H/W = constant

then (108/25)/12/x = (108/25)/18(150-x)

X = 90 = Milk, Water = 60

Final ratio = 3:2

QUESTION: 2

An Inlet pipe can fill a tank in 5 hours and an Outlet pipe can empty 4/7 of the same Tank in 4 hours. In the first hour only Inlet pipe is opened and in the second hour, only outlet pipe is opened. They have opened alternately every hour until the Tank is filled. Then in how many hours does the Tank gets filled?

Solution:

2 hours work = 1/5-1/7 = 2/35

34 hours work = 34/35

remaining work = 1/35

Now its inlet pipe turn = 1/35*5 = 1/7

= 34 hours + 60/7 min

QUESTION: 3

A Tank is already filled up to X% of its capacity. An Inlet pipe can fill Full Tank in 30 minutes and an Outlet pipe can empty Full Tank in 20 Minutes. Now both pipes are opened then the Tank is emptied in 24 Minutes. Then initially up to what % of its capacity is Tank filled?

Solution:

1/30 – 1/20 = -1/60

Full Tank can be emptied 60 Minutes

In 24 minutes 40% of Tank can be emptied.

QUESTION: 4

Two Inlet Pipes A and B together can fill a Tank in ‘X’ minutes. If A and B take 81 minutes and 49 minutes more than ‘X’ minutes respectively, to fill the Tank. Then They can fill the 5/7 of that Tank in how many minutes?

Solution:

Time taken by two pipes to fill full Tank is = √ab min = 63 min

5/7 Tank = 63*5/7 = 45 min

QUESTION: 5

Pipe A can fill a Tank in 18 Hours, Pipe B can empty a Tank in 12 Hours, Pipe C can fill Tank in 6 Hours. The Tank is already filled up to 1/6 of its capacity. Now Pipe A is opened in the First Hour alone, Pipe B is opened in the Second Hour alone and Pipe C is opened in the Third Hour alone. This cycle is repeated until the Tank gets filled. Then in How many Hours does the rest of Tank gets filled?

Solution:

In First Hour Tank filled = 1/6+1/18

Second Hour = 1/6+1/18-1/12

Third Hour = 1/6+1/18-1/12+1/6 = 11/36 is filled 25/36 is left

From then 3 hours work = 1/18-1/12+1/6 = 5/36

5*3 Hours = 5*5/36 = 25/36

Total = 5*3+3 = 18 Hours

QUESTION: 6

If the ratio of Rate of filling of two Pipes A and B is 3:2. If together they can fill a Tank 5/6th of Tank in 20 minutes. Then in how many does A alone can fill the Tank?

Solution:

5/6 tank = 20 Min

Full tank = 24 Min

1/2x+ 1/3x = 1/24

x = 20, A= 2x = 40 Min

QUESTION: 7

Pipe A, B and can fill a Full Tank in 24,36 and 48 Minutes respectively. All three Pipes are Opened simultaneously in a Tank which is already filled up to 1/6 of its capacity. A and B are opened for only First 6 Minutes and closed thereafter.Then C alone filled remaining Tank. Then in total how many Minutes does C filled the Tank?

Solution:

6*(1/24+1/36+1/48) + x/48 = 5/6

x = 14 Min

C = 6+14 = 20

QUESTION: 8

Pipe A and B can fill a Tank alone in 12 Hours and 6 Hours respectively. Another Pipe C can empty the same Tank alone in 9 Hours. In an empty Tank for the First hour, Pipe A is opened alone, Second Hour pipe B is opened alone, Third Hour pipe C is opened alone. This process is continued until the Tank is filled. Then Pipe A is opened for How many Hours?

Solution:

3 hours work = 1/12+ 1/6 – 1/9 = 5/36

7*3 hours work = 35/36

remaining work = 1/36

Now its pipe A turn = 1/36*12 = 1/3 hour

Total = 7 hours + 20 min

QUESTION: 9

Pipe A and B can fill a Tank alone in 48 Hours and 24 Hours respectively. Another Pipe C can empty the same Tank alone in 36 Hours. In an empty Tank for the First hour, Pipe A is opened alone, Second Hour pipe B is opened alone, Third Hour pipe C is opened alone. This process is continued until the Tank is filled. Then Pipe B is opened for How many Hours?

Solution:

3 Hours work = (1/48+1/24-1/36) = 5/144 28* 3hours = 140/144

remaining part = 4/144 = 1/36

Now it’s A turn = 1/36-1/48

= 1/144 left

Now it’s B turn = 1/144*24 = 1/6 hour = 10 min

Total B = 28 Hours + 10 Min

QUESTION: 10

Two Pipes A and B together can fill a Tank in ‘X’ minutes. If ‘A’ is Inlet Pipe can Fill the Tank alone in 40 minutes less than ‘X’ minutes and ‘B’ is Outlet pipe can empty the Tank alone in 30 minutes less than ‘X’ minutes. Then together they can fill the empty Tank in how many minutes?

Solution:

1/x-40 – 1/x-30 = 1/x

x = 60 min

QUESTION: 11

A Special pump can be used for filling as well as for emptying a Cistern. The capacity of the Cistern is 2400m³. The emptying capacity of the Cistern is 10m³ per minute higher than its filling capacity and the pump needs 8 minutes lesser to Cistern the tank than it needs to fill it. What is the filling capacity of the pump?

Solution:

Filling Capacity of the Pump = x m/min

Emptying Capacity of the pump = (x+10) m/min

2400/x – 2400/x+10 = 8

(x – 50) + (x + 60) = 0

x = 50

QUESTION: 12

Three pipes P, Q and R can fill a Cistern in 6 hours. After working at it together for 2 hours, R is closed and P and Q can fill the remaining part in 7 hours. The number of hours taken by R alone to fill the Cistern is

Solution:

Part filled in 2 hours = 2/6 = 1/3

Remaining Part = (1-1/3) = 2/3

(P + Q)’s 7 hour work = 2/3

(P + Q)’s 1 hour work = 2/21

R’s 1 hour work = (P + Q + R) 1 hour work – (P + Q) 1 hour work

= (1/6 – 2/21) = 1/14 = 14 hours

QUESTION: 13

A Cistern is two-fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open,how long will it take to empty or fill the tank completely?

Solution:

pipe B is faster than pipe A and so,the tank will be emptied.

part to be emptied = 2/5

part emptied by (A+B) in 1 minute= (1/6 – 1/10) = 1/15

1/15 : 2/5 :: 1: x

2/5 * 15 = 6 minutes.

QUESTION: 14

If a pipe A can fill a tank 3 times faster than pipe B. If both the pipes can fill the tank in 32 minutes, then the slower pipe alone will be able to fill the tank in?

Solution:

Time is taken by pipe A = x

Time is taken by pipe B = x/3

1/x + 3/x = 1/32

x = 128 minutes

QUESTION: 15

A large cistern can be filled by two pipes P and Q in 15 minutes and 20 minutes respectively. How many minutes will it take to fill the Cistern from an empty state if Q is used for half the time and P and Q fill it together for the other half?

Solution:

Part filled by P and Q = 1/15 + 1/20 = 7/60

Part filled by Q = 1/20

x/2(7/60 + 1/20) = 12 minutes

QUESTION: 16

A pipe can fill a cistern in 16 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the cistern completely?

Solution:

In One hour pipe can fill = 1/16

Time is taken to fill half of the tank = 1/2 * 16 = 8 hours

Part filled by four pipes in one hour = (8*1/16) = 1/2

Required Remaining Part = 1/2

Total time = 8 + 1 = 9

QUESTION: 17

Two pipes P and Q are opened together to fill a tank. Both the pipes fill the tank in time “x” If Q separately took 25 minutes more time than “x” to fill the tank and Q took 49 minutes more time than “x” to fill the tank, then find out the value of x?

Solution:

Time is taken to fill the tank by both Pipes x = √a*b

x = √25*49 = 5 * 7 = 35

QUESTION: 18

Three taps P, Q and R can fill a tank in 12, 15 and 20 hours respectively. If P is open all the time and Q, R are open for one hour each alternatively, the tank will be full in

Solution:

(P + Q)’s 1 hour work = 1/12 + 1/15 = 3/20

(P + R)’s 1 hour work = 1/12 + 1/20 = 2/15

For 2 hrs = (3/20 + 2/15) = 17/60

For 6 hrs = (3*17/60) = 17/20

Remaining Part = 1 – 17/20 = 3/20 filled by P and Q in 1 hour

QUESTION: 19

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?

Solution:

Total Capacity = 90L.

Tank filled in 1 minute by A = 3L

Tank filled in 1 minute by B = 15L

The capacity of the tank filled with both A and B in 1 minute = 18L.

overflow = 90/18 = 5 minutes.

QUESTION: 20

Two pipes P and Q can fill a cistern in 10 hours and 20 hours respectively. If they are opened simultaneously. Sometimes later, tap Q was closed, then it takes total 5 hours to fill up the whole tank. After how many hours Q was closed?

Solution:

Pipe P Efficiency = 100/10 = 10%

Pipe Q Efficiency = 100/20 = 5%

Net Efficiency = 15%

15x + 10(5-x) = 100

x = 10

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