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- Question
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
- Correct Answer
- 14
ExplanationTags: Bank ExamsPart 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.
Pipes and Cistern problems
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- 1. 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]
- 2. 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.
- 3. Two number are in the ratio 3 : 5. If 9 is subtracted from each, the new numbers are in the ratio 12 : 23. The smaller number is:
Options- A. 27
- B. 33
- C. 49
- D. 55 Discuss
Correct Answer: 33
Explanation:
Let the numbers be 3x and 5x.Then, 3x - 9 = 12 5x - 9 23 ⟹ 23(3x - 9) = 12(5x - 9)
⟹ 9x = 99
⟹ x = 11.
∴ The smaller number = (3 x 11) = 33.
- 4. If 0.75 : x :: 5 : 8, then x is equal to:
Options- A. 1.12
- B. 1.2
- C. 1.25
- D. 1.30 Discuss
Correct Answer: 1.2
Explanation:
(x x 5) = (0.75 x 8) ⟹ x = ❨ 6 ❩ = 1.20 5 - 5. In a mixture 60 litres, the ratio of milk and water 2 : 1. If this ratio is to be 1 : 2, then the quanity of water to be further added is:
Options- A. 20 litres
- B. 30 litres
- C. 40 litres
- D. 60 litres Discuss
Correct Answer: 60 litres
Explanation:
Quantity of milk = ❨ 60 x 2 ❩litres = 40 litres. 3 Quantity of water in it = (60- 40) litres = 20 litres.
New ratio = 1 : 2
Let quantity of water to be added further be x litres.
Then, milk : water = ❨ 40 ❩ . 20 + x Now, ❨ 40 ❩ = 1 20 + x 2 ⟹ 20 + x = 80
⟹ x = 60.
∴ Quantity of water to be added = 60 litres.
- 6. 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]
- 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?
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.
- 8. 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.
- 9. 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.
- 10. 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
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