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- Question
A pump can fill a tank with water in 2 hours. Because of a leak, it took 2⅓ hours to fill the tank. The leak can drain all the water of the tank in:
Options- A.
4 1 hours 3 - B. 7 hours
- C. 8 hours
- D. 14 hours
- Correct Answer
- 14 hours
ExplanationWork done by the leak in 1 hour = ❨ 1 - 3 ❩ = 1 . 2 7 14 ∴ Leak will empty the tank in 14 hrs.
Pipes and Cistern problems
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- 1. 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 three pipes are opened together, then the tank will be filled in:
Options- A.
1 13 hours 17 - B.
2 8 hours 11 - C.
3 9 hours 17 - D.
4 1 hours 2
Discuss
Correct Answer:3 9 hours 17
Explanation:
Net part filled in 1 hour ❨ 1 + 1 - 1 ❩ = 17 . 5 6 12 60 ∴ The tank will be full in 60 hours i.e., 3 9 hours. 17 17 - 2. 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.
- 3. 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 Discuss
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.
- 4. 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 - 5. 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.
- 6. 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?
Options- A. 10 min. 20 sec.
- B. 11 min. 45 sec.
- C. 12 min. 30 sec.
- D. 14 min. 40 sec. Discuss
Correct Answer: 14 min. 40 sec.
Explanation:
Part filled in 4 minutes = 4 ❨ 1 + 1 ❩ = 7 . 15 20 15 Remaining part = ❨ 1 - 7 ❩ = 8 . 15 15 Part filled by B in 1 minute = 1 20 ∴ 1 : 8 :: 1 : x 20 15 x = ❨ 8 x 1 x 20 ❩ = 10 2 min = 10 min. 40 sec. 15 3 ∴ The tank will be full in (4 min. + 10 min. + 40 sec.) = 14 min. 40 sec.
- 7. 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?
Options- A. 15 min
- B. 20 min
- C. 27.5 min
- D. 30 min Discuss
Correct Answer: 30 min
Explanation:
Part filled by (A + B) in 1 minute = ❨ 1 + 1 ❩ = 1 . 60 40 24 Suppose the tank is filled in x minutes.
Then, x ❨ 1 + 1 ❩ = 1 2 24 40 ⟹ x x 1 = 1 2 15 ⟹ x = 30 min.
- 8. 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:
Options- A. 81 min.
- B. 108 min.
- C. 144 min.
- D. 192 min. Discuss
Correct Answer: 144 min.
Explanation:
Let the slower pipe alone fill the tank in x minutes.Then, faster pipe will fill it in x minutes. 3 ∴ 1 + 3 = 1 x x 36 ⟹ 4 = 1 x 36 ⟹ x = 144 min.
- 9. A merchant has 1000 kg of sugar, part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantity sold at 18% profit is:
Options- A. 400 kg
- B. 560 kg
- C. 600 kg
- D. 640 kg Discuss
Correct Answer: 600 kg
Explanation:
By the rule of alligation, we have:Profit on 1st part Profit on 2nd part 8% Mean Profit
14%18% 4 6 Ration of 1st and 2nd parts = 4 : 6 = 2 : 3
∴ Quantity of 2nd kind = ❨ 3 x 1000 ❩kg = 600 kg. 5 - 10. The cost of Type 1 rice is Rs. 15 per kg and Type 2 rice is Rs. 20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2 : 3, then the price per kg of the mixed variety of rice is:
Options- A. Rs. 18
- B. Rs. 18.50
- C. Rs. 19
- D. Rs. 19.50 Discuss
Correct Answer: Rs. 18
Explanation:
Let the price of the mixed variety be Rs. x per kg.By rule of alligation, we have:
Cost of 1 kg of Type 1 rice Cost of 1 kg of Type 2 rice Rs. 15 Mean Price
Rs. xRs. 20 (20 - x) (x - 15) ∴ (20 - x) = 2 (x - 15) 3 ⟹ 60 - 3x = 2x - 30
⟹ 5x = 90
⟹ x = 18.
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