Pipes and Cistern problems
- 1. 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?
Options- A. 20 hours
- B. 25 hours
- C. 35 hours
- D. Cannot be determined
- E. None of these Discuss
Correct Answer: 35 hours
Explanation:
Suppose pipe A alone takes x hours to fill the tank.
| Then, pipes B and C will take | x | and | x | hours respectively to fill the tank. |
| 2 | 4 |
| ∴ | 1 | + | 2 | + | 4 | = | 1 |
| x | x | x | 5 |
| ⟹ | 7 | = | 1 |
| x | 5 |
⟹ x = 35 hrs.
- 2. 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?
Options- A. 1 hour
- B. 2 hours
- C. 6 hours
- D. 8 hours Discuss
Correct Answer: 6 hours
Explanation:
Let the cistern be filled by pipe A alone in x hours.
Then, pipe B will fill it in (x + 6) hours.
| ∴ | 1 | + | 1 | = | 1 |
| x | (x + 6) | 4 |
| ⟹ | x + 6 + x | = | 1 |
| x(x + 6) | 4 |
⟹ x2 - 2x - 24 = 0
⟹ (x -6)(x + 4) = 0
⟹ x = 6. [neglecting the negative value of x]
- 3. Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 7 hours. The number of hours taken by C alone to fill the tank is:
Options- A. 10
- B. 12
- C. 14
- D. 16 Also asked in: Bank Exams
Correct Answer: 14
Explanation:
| Part filled in 2 hours = | 2 | = | 1 |
| 6 | 3 |
| Remaining part = | ❨ | 1 - | 1 | ❩ | = | 2 | . |
| 3 | 3 |
| ∴ (A + B)'s 7 hour's work = | 2 |
| 3 |
| (A + B)'s 1 hour's work = | 2 |
| 21 |
∴ C's 1 hour's work = { (A + B + C)'s 1 hour's work } - { (A + B)'s 1 hour's work }
| = | ❨ | 1 | - | 2 | ❩ | = | 1 |
| 6 | 21 | 14 |
∴ C alone can fill the tank in 14 hours.
- 4. 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:
Options- A. 6 hours
- B. 10 hours
- C. 15 hours
- D. 30 hours Discuss
Correct Answer: 15 hours
Explanation:
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 | + | 1 | = | 1 |
| x | (x - 5) | (x - 9) |
| ⟹ | x - 5 + x | = | 1 |
| x(x - 5) | (x - 9) |
⟹ (2x - 5)(x - 9) = x(x - 5)
⟹ x2 - 18x + 45 = 0
(x - 15)(x - 3) = 0
⟹ x = 15. [neglecting x = 3]
- 5. 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?
Options- A. 12 min
- B. 15 min
- C. 25 min
- D. 50 min Discuss
Correct Answer: 12 min
Explanation:
| Part filled by A in 1 min = | 1 | . |
| 20 |
| Part filled by B in 1 min = | 1 | . |
| 30 |
| Part filled by (A + B) in 1 min = | ❨ | 1 | + | 1 | ❩ | = | 1 | . |
| 20 | 30 | 12 |
∴ Both pipes can fill the tank in 12 minutes.
- 6. Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternately, the tank will be full in:
Options- A. 6 hours
- B.
6 2 hours 3 - C. 7 hours
- D.
7 1 hours 2
Discuss
Correct Answer: 7 hours
Explanation:
| (A + B)'s 1 hour's work = | ❨ | 1 | + | 1 | ❩ | = | 9 | = | 3 | . |
| 12 | 15 | 60 | 20 |
| (A + C)'s hour's work = | ❨ | 1 | + | 1 | ❩ | = | 8 | = | 2 | . |
| 12 | 20 | 60 | 15 |
| Part filled in 2 hrs = | ❨ | 3 | + | 2 | ❩ | = | 17 | . |
| 20 | 15 | 60 |
| Part filled in 6 hrs = | ❨ | 3 x | 17 | ❩ | = | 17 | . |
| 60 | 20 |
| Remaining part = | ❨ | 1 - | 17 | ❩ | = | 3 | . |
| 20 | 20 |
| Now, it is the turn of A and B and | 3 | part is filled by A and B in 1 hour. |
| 20 |
∴ Total time taken to fill the tank = (6 + 1) hrs = 7 hrs.
- 7. Two pipes A and B can fill a cistern in 37½ 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:
Options- A. 5 min.
- B. 9 min.
- C. 10 min.
- D. 15 min. Discuss
Correct Answer: 9 min.
Explanation:
Let B be turned off after x minutes. Then,
Part filled by (A + B) in x min. + Part filled by A in (30 -x) min. = 1.
| ∴ x | ❨ | 2 | + | 1 | ❩ | + (30 - x). | 2 | = 1 |
| 75 | 45 | 75 |
| ⟹ | 11x | + | (60 -2x) | = 1 |
| 225 | 75 |
⟹ 11x + 180 - 6x = 225.
⟹ x = 9.
- 8. 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?
Options- A.
5 11 - B.
6 11 - C.
7 11 - D.
8 11
Discuss
Correct Answer:
| 6 |
| 11 |
Explanation:
| Part filled by (A + B + C) in 3 minutes = 3 | ❨ | 1 | + | 1 | + | 1 | ❩ | = | ❨ | 3 x | 11 | ❩ | = | 11 | . |
| 30 | 20 | 10 | 60 | 20 |
| Part filled by C in 3 minutes = | 3 | . |
| 10 |
| ∴ Required ratio = | ❨ | 3 | x | 20 | ❩ | = | 6 | . |
| 10 | 11 | 11 |
- 9. 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:
Options- A. 60 gallons
- B. 100 gallons
- C. 120 gallons
- D. 180 gallons Also asked in: AIEEE, Bank Exams, CAT, Bank Clerk, Bank PO
Correct Answer: 120 gallons
Explanation:
| Work done by the waste pipe in 1 minute = | 1 | - | ❨ | 1 | + | 1 | ❩ |
| 15 | 20 | 24 |
| = | ❨ | 1 | - | 11 | ❩ |
| 15 | 120 |
| = - | 1 | . [-ve sign means emptying] |
| 40 |
| ∴ Volume of | 1 | part = 3 gallons. |
| 40 |
Volume of whole = (3 x 40) gallons = 120 gallons.
- 10. A tap can fill a tank in 6 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?
Options- A. 3 hrs 15 min
- B. 3 hrs 45 min
- C. 4 hrs
- D. 4 hrs 15 min Discuss
Correct Answer: 3 hrs 45 min
Explanation:
Time taken by one tap to fill half of the tank = 3 hrs.
| Part filled by the four taps in 1 hour = | ❨ | 4 x | 1 | ❩ | = | 2 | . |
| 6 | 3 |
| Remaining part = | ❨ | 1 - | 1 | ❩ | = | 1 | . |
| 2 | 2 |
| ∴ | 2 | : | 1 | :: 1 : x |
| 3 | 2 |
| ⟹ x = | ❨ | 1 | x 1 x | 3 | ❩ | = | 3 | hours i.e., 45 mins. |
| 2 | 2 | 4 |
So, total time taken = 3 hrs. 45 mins.
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