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- Question
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
- Correct Answer
- 30 min
ExplanationPart 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.
Pipes and Cistern problems
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- 1. 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.
- 2. 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 Discuss
Correct Answer: 14 hours
Explanation:
Work done by the leak in 1 hour = ❨ 1 - 3 ❩ = 1 . 2 7 14 ∴ Leak will empty the tank in 14 hrs.
- 3. 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 - 4. 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.
- 5. 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.
- 6. 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.
- 7. 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 - 8. 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.
- 9. A milk vendor has 2 cans of milk. The first contains 25% water and the rest milk. The second contains 50% water. How much milk should he mix from each of the containers so as to get 12 litres of milk such that the ratio of water to milk is 3 : 5?
Options- A. 4 litres, 8 litres
- B. 6 litres, 6 litres
- C. 5 litres, 7 litres
- D. 7 litres, 5 litres Discuss
Correct Answer: 6 litres, 6 litres
Explanation:
Let the cost of 1 litre milk be Re. 1Milk in 1 litre mix. in 1st can = 3 litre, C.P. of 1 litre mix. in 1st can Re. 3 4 4 Milk in 1 litre mix. in 2nd can = 1 litre, C.P. of 1 litre mix. in 2nd can Re. 1 2 2 Milk in 1 litre of final mix. = 5 litre, Mean price = Re. 5 8 8 By the rule of alligation, we have:
C.P. of 1 litre mixture in 1st can C.P. of 1 litre mixture in 2nd can 3 4 Mean Price
5 8 1 2 1 8 1 8 ∴ Ratio of two mixtures = 1 : 1 = 1 : 1. 8 8 So, quantity of mixture taken from each can = ❨ 1 x 12 ❩ = 6 litres. 2 - 10. In what ratio must a grocer mix two varieties of pulses costing Rs. 15 and Rs. 20 per kg respectively so as to get a mixture worth Rs. 16.50 kg?
Options- A. 3 : 7
- B. 5 : 7
- C. 7 : 3
- D. 7 : 5 Discuss
Correct Answer: 7 : 3
Explanation:
By the rule of alligation:Cost of 1 kg pulses of 1st kind Cost of 1 kg pulses of 2nd kind Rs. 15 Mean Price
Rs. 16.50Rs. 20 3.50 1.50 ∴ Required rate = 3.50 : 1.50 = 7 : 3.
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