Pipes and Cisterns Problems for Competitive Exams

Vikram Singh3 years ago 6.4K Views Join Examsbook

Pipes and Cisterns Problems are part of the aptitude section. In these problems, students have to find the correct answers according to the situation or statement. Pipes and Cisterns problems are not difficult to solve, you just need to understand the problem to solve it.

For your better preparation, here I am giving you Pipes and Cisterns Problems with solutions which helps you to understand this topic as well as its problems. You can know how to use Formulas in Pipes and Cisterns Problems while solving.

Pipes and Cisterns Problems with Solutions

Q.1. Two pipes A and B can separately fill a cistern in 60 minutes and 75 minutes respectively. There is a third pipe in the bottom of the cistern to empty it. If all the tree pipes are simultaneously opened, then the cistern is full in 50 minutes. In how much time the third pipe alone can empty the cistern?

(A) 80 min

(B) 100 min

(D) 120 min

Show Answer

Ans . B

Solution

work done by the third pipe in 1 min.

$$ = {1\over 50}- \left( {1\over60}+{1\over 75} \right)= \left( {1\over 50}-{3\over 100} \right)= -{1\over 100} [ - \ ve \ sign \ means \ emptying] $$

∴ The third pipe empty alone can empty the cistern in 100 min.

Q.2. A Cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 9 hours. If both the taps are opened simultaneously then after how much time will the cistern get filled?

(A) 4.5 hrs

(B) 5 hrs

(D) 7.2 hrs

Show Answer

Ans . D

Solution

Net part filled in 1 hour = $$ \left( {1\over 4}-{1\over 9}= {5\over 36} \right). $$

⸫ The cistern will be filled in hrs i.e, 7.2 hrs.

Q.3. A pump can fill a tank with water in 2 hours. Because of a leak, it took hours to fill the tank. The leak can drain all the water of the tank in:

(A) hrs

(B) 8 hrs

(D) 14 hrs

Show Answer

Ans . D

Solution

Work done by the leak in 1 hour = $$ \left( {1\over 2} - {3\over 7} \right)= {1\over 14} $$

∴ Leak will empty the tank in 14 hrs.

Q.4. A tap can fill a tank in 6 hours. After the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?

(A) 3 hrs

(B) 3 hrs 45 min

(D) 5 hrs 15.

Show Answer

Ans . B

Solution

Time and taken by one tap to fill half the tank = 3 hrs.

Part filled by the four taps in 1 hours = $$ \left( 4 × {1\over 6} \right)= {2\over 3}. $$

Remaining part = $$ \left( 1 - {1\over 2} \right)= {1\over 2} $$

$$ ∴ {2\over 3}: {1\over 2}:: 1: x \ or\ x= \left( {1\over2}×1×{3\over 2} \right)= {3\over 4} \ hrs \ i.e, \ 45 \ mins $$

Q.5. 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) 80 min

(B) 108 min

(D 180 min

Show Answer

Ans . C

Solution

Let the slower pipe alone fill the tank in x minutes.

Then, faster pipe will fill it in minutes.

⸫ $$ {1\over x}+{3\over x}= {1\over 36} $$

$$ ⟺ {4\over x} = {1\over 36} ⟺ x=144 min $$

Q.6. A water tank 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?

(A) 6 min to empty

(B) 6 min to fill

(D) 8 min to fill

(E) None of these

Show Answer

Ans . A

Solution

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

Part to be emptied = .

Part emptied by (A+B) in 1 minute $$= \left( {1\over 6}-{1\over10} \right)= {1\over 15} $$

$$∴ {1\over 15}: {2\over 5}::1:x \ or \ x = \left({2\over5}×1×{15} \right)=6 \ min. $$

So, the tank will be emptied in 6 min

Q.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) 15 hrs

(B) 25 hrs

(D)45

(E) None of these

Show Answer

Ans . C

Solution

Suppose pipe A alone takes x hours to fill the tank.

Then, pipe B and C will take and hours respectively to fill the tank.

$$ {1\over x}+{2\over x}+{4\over x}={1\over 5}$$

$$⟺ {7\over x}= {1\over 5}⟺ x = 35 \ hrs $$

Q.8. Pipe A can fill a tank in 5 hours, pipe B in 10 hours and pipe C in 30 hours. If all the pipes are open, in how many hours will the tank be filled?

(A) 1

(B) 2.5

(D) 3.5

Show Answer

Ans . C

Solution

Part filled by (A+B+C) in 1 hour = $$ \left( {1\over 5}+{1\over 10}+{1\over 30} \right)= {1\over 3} $$∴ All the three pipes together will fill the tank in 3 hours.

Q.9. 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 hrs

(B) 12 hrs

(D) 30 hrs

Show Answer

Ans . C

Solution

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.

$$ ∴ {1\over x}+{1\over(x-5)}={1\over(x-9)} $$

$$⟺ \ {x-5+x\over x(x-5) }= {1\over (x-9)} $$

$$ ⟺ (2x -5)(x-9)=x(x-5)⟺ x^2-18x+45=0$$

$$ (x-15)(x-3)=0⟺ x=15. $$

Q.10. 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 tree pipe are opened together, then the tank will be filled in:

(A) hours