Time and Work|| Chapter -3: Pipe and Cistern

✍️📚Introduction: He Zirlai Pipes and Cisterns hi Competitive exam na ah a pawimawh em em a ni.Competitive exam hrang hrang a pawimawh thin te lak khawm ani a Mizo leh english hman a ni bawk.Heng a hnuai ah hian hrilhfiahna pawimawh tak tak te ka dah tel bawk a, example ka lak ho pawh hi Question pawimawh tak tak lo chhuak tawh thin a ni e.Math ah chuan eng tin nge kan solve ang tih ngaihtuah thiam hi a pawimawh em em a heng question ka lo solve sa te hi hna exam ah a chhuak ngei ngei dawn tihna lam ni lovin he mi chapter atanga problem awm thei tlangpui in zirtirna zawk a ni e.

— Elisa Lalrinngheta(Zo Guide)

🕵️Concept:

Pipes leh Cistern chungchang zawhnate hi hun (time), hna (work), leh a luan dan (flow) chapter hnuaia mi an ni. Heng zawhnate hian pipe pakhat emaw a aia tam emaw hmanga tui tank (cistern) khah hun chhung emaw, a ruah hun chhung emaw chhut a kawk a ni. Pipe thenkhatin tank an thun khat a, a thenin an leihruak thung. Heng zawhna te hi tui luh dan (inflow) leh tui chhuah dan (outflow) zat (rate) thila innghat an ni.

✅Thumal Pawimawh leh a Hrilhfiahna:

1.Inlet Pipe (Tui thunna pipe):

Pipe tank-a tui thun khattu.

Tank-ah tui a thun belh a, tui a ti sang thin.

2.Outlet Pipe (Tui paihna/chhuahna pipe):

Pipe tank tihruaktu (tui leihruaktu).

Tank atangin tui a paih chhuak a, tui a ti hniam thin.

3.Cistern emaw Tank:

Tui dahkhawmna, a khah hun emaw a ruah hun emaw chhut nana kan hman chu.

4.Capacity of the Tank (Tank dawn hlawk zawng):

Tui (emaw thil tui dang) tank a awm leng zawng zawng, a tlangpuiin liters emaw cubic meters-in an teh thin.

✅Zawhna Chinfel Dan - A Kalsiam leh a Thuruk te

Exam hmachhawn tur te tan pipes leh cistern chungchanga zawhna chinfel dan thuruk (tips and tricks) hrang hrang a hnuaiah hian tarlan a ni:

Tip 1: Pipe pakhatin tank chu x (hour) chhungin a thun khat thei a, pipe dang leh chuan y chhungin a thun khat thei bawk a nih chuan, pipe pahnihte’n 1 hr chhunga tank an thun khah zat chu:

English Version:

How to Solve Question Based on Pipes and Cistern - Know all Tips and Tricks -

Candidates can find different tips and tricks from below for solving the questions related to pipes and cistern.

Tip 1: If a pipe can fill a tank in x hours and another pipe can fill it in y hours, then the fraction of tank filled by both pipes together in 1 hour = 1/x + 1/y = x +y/xy

Tip 2: Pipe pakhatin tank chu darkar x-ah a tihkhah theih a, pipe dang pakhatin darkar

y-ah a tihruah theih chuan, darkar 1 chhunga an pahniha an thawh ruala tank khah zawng zat chu

a ni.

📝Formula Pawimawh-te:

1.Tank tihkhah dan (Filling the Tank):

Inlet pipe (tui luhna pipe)-in tank chu darkar A chhunga a tihkhah theih chuan, darkar 1 chhunga tui khah zat chu =1/A a ni.

2.Tank tihruah dan (Emptying the Tank):

Outlet pipe (tui chhuahna pipe)-in tank chu darkar B chhunga a tihruah theih chuan, darkar 1 chhunga tui chhuak zat chu =1/B a ni.

3.A luh leh chhuah zat hlawm (Net Inflow or Outflow):

Tui luhna leh chhuahna pipe-te a ruala hawn an nihin:

Darkar 1 chhunga tank khah zat = (Darkar 1 chhunga inlet pipe-in a tihkhah zat) - (Darkar 1 chhunga outlet pipe-in a tihruah zat).

🕵️Formula: 1/A –1/B (A hi a khah hun chhung a ni a, B hi ruah hun chhung a ni).

4.Pipe tam tak a nihin (Multiple Pipes):

Pipe tam tak an awm chuan, darkar 1 chhunga tui khah zat emaw ruah zat emaw chu pipe zawng zawngte chak zawng belhkhawm (sum) emaw paihkhawm (difference) emaw a ni.

5.Pipe pahnih hmanga Tank tihkhah emaw tihruah emaw:

• Inlet pipe pahnih (pakhat darkar A-a khat thei leh pakhat darkar B-a khat thei) an thawh dun chuan, darkar 1 chhunga tank khah zat chu: 1/A +1/B a ni.

• Inlet pipe leh outlet pipe an thawh dun a, inlet pipe-in a tihkhah chak zawk chuan, darkar 1 chhunga tank khah zat chu:

1/A – 1/B a ni.

6.Tank a khah vek hun (Tank Completely Filled):

Darkar 1 chhunga tank khah zat chu 1/x a nih chuan, tank khah vekna atana hun ngai zat chu = x darkar a ni.

📝✅ PROBLEM HO HI CHU ENGLISH VEKIN KA LO SOLVE ANG NGE

📝Types of Problems:

1. One Pipe Filling the Tank:

A single pipe fills the tank at a fixed rate.

🕵️Example 1: A pipe can fill a tank in 6 hours. How much part of the tank is filled in 1 hour?

Solution:

Part of the tank filled in 1 hour = 1/6.

2. One Pipe Emptying the Tank: A single pipe empties the tank at a fixed rate.

🕵️Example 2: An outlet pipe can empty a full tank in 8 hours. How much part of the tank is emptied in 1 hour?

Solution:

Part of the tank emptied in 1 hour = 1/8.

3. Two Pipes Working Together: Two inlet pipes fill the tank simultaneously.

🕵️Example 3: One pipe fills the tank in 4 hours and another in 6 hours. How much time will they take to fill the tank together?

Solution:

Part of the tank filled by the first pipe in 1 hour = 1/4. Part of the tank filled by the second pipe in 1 hour = 1/6. Together, part filled in 1 hour = 1/4 + 1/6 (3+2)/12 = 5/12. Thus, the tank will be filled in 12/5 = 2.4 hours.

4. Inlet and Outlet Pipes Working Together:

Both inlet and outlet pipe are open at the same time.

🕵️Example 4: A pipe can fill a tank in 3 hours, but an outlet pipe can empty it in 4 hours. If both are opened simultaneously, how much time will it take to fill the tank?

5. Pipes Operating Intermittently:

Some problems involve pipes working for a few hours and then stopping or operating in shifts.

6. Cistern Leaks:

Some problems involve tanks with leaks, meaning water is lost while filling.

Example 6: A pipe can fill a tank in 8 hours, but due to a leak, it takes 10 hours to fill. How long will the leak alone take to empty the full tank?

Solution:

Example 7: Pipe K can fill a tank in 25 hours while pipe L can empty the same tank in 40 hours, find the time taken for tank to fill if pipe L is closed after tank is filled 3/4th.

🕵️Example 8: What is the time taken by two pipes M and N together to fill a tank completely given that pipes M and N can fill the tank in 42 and 56 minutes respectively?

Solutions: Part filled by pipe M in 1 minute = (1/42) Part filled by pipe N in 1 minute = (1/56) Part filled by pipe M and N together in 1 minute (1/42)+(1/56) →1/24 ..

The correct answer is 24 minutes.

🕵️Example 9: Three pipes A, B, and C can fill a tank in 10 minutes, 12 minutes, and 15 minutes respectively. The pipe B is closed 3/2 minutes before the tank is filled. In what time the tank will full?

Solutions: Let the capacity of the tank be 60 units (LCM of 10, 12, and 15 = 60) Efficiency, A = 60/10 = 6 units/min,

B = 60/12 = 5 units/min,

C = 60/15 = 4 units/min

Pipe B is closed 3/2 min before the tank fill (A+C) work for 3/2 min extra Tank filled in 3/2 min = 10 x 3/2 = 15 unit Remaining part of tank = 60-15 = 45 unit

Example 10: The tank has two taps. Tap A is to fill the tank and tap B is to empty the tank. If only tap A can fill the tank in 35 hours, only tap B can empty the filled tank completely in 70 hours. Find how many hours it will take to fill the half empty tank completely.

Solution:

📝✅UPSC Old Questions Solved:

🕵️. Two pipes A and B can independently fill a tank completely in 20 and 30 minutes respectively. If both the pipes are opened simultaneously, how much time will they take to fill the tank completely? [CSAT 2015]

(a) 10 minutes

(b) 12 minutes

(d) 25 minutes

Solution:

Given that,

Two pipes A and B can independently fill a tank completely in 20 and 30 minutes respectively.

Both the pipes are opened simultaneously.

Now,

Total work done = LCM of 20 and 30 = 60

Thus

Efficiency of pipe A = 60/20 = 3

Efficiency of Pipe B = 60/30 = 2

Total efficiency = 3 + 2 = 5

Therefore, total time taken = 60/5 = 12 minutes

Hence option (b) is correct

📝Practice Questions:

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

B.6

C.7

D.8

2.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

3.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

4.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

5.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

6.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

7.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

8.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.

9.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.

10.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 key:

1.Solutions: