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- Question
Three taps I, J and K can fill a tank in 20,30and 40 minutes respectively. All the taps are opened simultaneously and after 5 minutes tap A was closed and then after 6 minutes tab B was closed .At the moment a leak developed which can empty the full tank in 70 minutes. What is the total time taken for the completely full ?
Options- A. 24.315 minutes
- B. 26.166 minutes
- C. 22.154 minutes
- D. 24 minutes
- Correct Answer
- 26.166 minutes
ExplanationUpto first 5 minutes I, J and K will fill => 5[(1/20)+(1/30)+(1/40)] = 65/120
For next 6 minutes, J and K will fill => 6[(1/30)+(1/40)] = 42/120
So tank filled upto first 11 minutes = (65/120) + (42/120) = 107/120
So remaining tank = 13/120
Now at the moment filling with C and leakage @ 1/60 per minute= (1/40) - (1/70) = 3/280.
So time taken to fill remaining 13/120 tank =(13/120) /(3/280) = 91/6 minutesHence total time taken to completely fill the tank = 5 + 6 + 91/6 = 26.16 minutes.
- 1. A water tank in a village is normally filled in 8 hours but takes 2 hours longer to fill because of a leak in its bottom. If the tank is full, in how many hrs will the leak empty it ?
Options- A. 34 hrs
- B. 36 hrs
- C. 38 hrs
- D. 40 hrs Discuss
- 2. One fill pipe A is 3 times faster than second fill pipe B and takes 32 minutes less than the fill pipe B. When will the cistern be full if both pipes are opened together?
Options- A. 6 min
- B. 8 min
- C. 12 min
- D. 10 min Discuss
- 3. 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. 4 hrs 15 min
- B. 3 hrs 24 min
- C. 4 hrs 51 min
- D. 3 hrs 45 min Discuss
- 4. The ratio of efficiencies of two filling pipes is 4 : 5. There is a third emptying pipe which efficiency is two third of the average efficiency of first two filling pipes can empty a filled tank in 36 minutes. In how much time both the filling pipes can fill the tank when it is empty?
Options- A. 16 min
- B. 12 min
- C. 14 min
- D. 20 min Discuss
- 5. Pipe A can fill a tank in 16 minutes and pipe B cam empty it in 24 minutes. If both the pipes are opened together after how many minutes should pipe B be closed, so that the tank is filled in 30 minutes ?
Options- A. 21 min
- B. 24 min
- C. 20 min
- D. 22 min Discuss
- 6. A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 4 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold ?
Options- A. 360 lit
- B. 480 lit
- C. 320 lit
- D. 420 lit Discuss
- 7. Two filling taps P and Q together can fill a tank with rate of 40 lit/min and 60 lit/min respectively in 8 min. If a waste tap can empty the filled tank in 32 min, then what is the rate of waste tap ?
Options- A. 34 lit/min
- B. 25 lit/min
- C. 22 lit/min
- D. 18 lit/min Discuss
- 8. Pipe K fills a tank in 30 minutes. Pipe L can fill the same tank 5 times as fast as pipe K. If both the pipes were kept open when the tank is empty, how much time will it take for the tank to overflow ?
Options- A. 3 minutes
- B. 2 minutes
- C. 4 minutes
- D. 5 minutes Discuss
- 9. A Tank is normally filled in 9 hours but takes four hours longer to fill because of a leak in its bottom. If the tank is full, the leak will empty it in ?
Options- A. 32.5 hrs
- B. 29.25 hrs
- C. 30.30 hrs
- D. 31 hrs Discuss
- 10. A water tank has holes. The 1st hole alone empties the tank in 9 min and 2nd hole alone empties the tank in 6 min. If water leaks out at a constant rate, how many min does it take if both the holes together empty the tank?
Options- A. 3 3/5
- B. 3/5
- C. 3 1/5
- D. 3 2/5 Discuss
Pipes and Cistern problems
Search Results
Correct Answer: 40 hrs
Explanation:
The time taken by the leak to empty the tank =
Therefore, the leak empties the tank in 40 hours.
Correct Answer: 12 min
Explanation:
Let pipe A takes p min to fill
Then,
pipe B takes 3p min to fill
=> 3p - p = 32
=> p = 16 min => 3p = 48 min
Required, both pipes to fill = (48 x 16)/(48 + 16) min = 12 min.
Correct Answer: 3 hrs 45 min
Explanation:
Time taken by one tap to fill half of the tank = 3 hrs.
Part filled by the taps in 1 hour = 4 x 1/6 = 2/3
Remaining part = 1 - 1/2 = 1/2
2/3 : 1/2 :: 1 : p
p = 1/2 x 1 x 3/2 = 3/4 hrs. i.e., 45 min
So, total time taken = 3 hrs 45 min.
Correct Answer: 12 min
Explanation:
Let the efficiencies of filling pipes is 4p and 5p respectively.
Efficiency of pipe which empty the tank = 2/3 x 9p/2 = 3p
Total work = 3p x 36 = 108p
Time to fill the tank by both the pipes = 108p/9p = 12 min.
Correct Answer: 21 min
Explanation:
Let the pipe B be closed after 'K' minutes.
30/16 - K/24 = 1 => K/24 = 30/16 - 1 = 14/16
=> K = 14/16 x 24 = 21 min.
Correct Answer: 480 lit
Explanation:
1/k - 1/20 = -1/24
k = 120
120 x 4 = 480
Therefore, the capacity of the cistern is 480 liters.
Correct Answer: 25 lit/min
Explanation:
Given that the waste tap can empty the filled tank in 32 min.
Now, the rate at which the waste tap can empty the tank = (40 + 60)8/32 = 100/4 = 25 lit/min.
Correct Answer: 5 minutes
Explanation:
Let the total capacity of tank be 90 liters.
Capacity of tank filled in 1 minute by K = 3 liters.
Capacity of tank filled in 1 minute by L = 15 liters.
Therefore, capacity of the tank filled by both K and L in 1 minute = 18 liters.
Hence, time taken by both the pipes to overflow the tank = 90/18 = 5 minutes.
Correct Answer: 29.25 hrs
Explanation:
Let the leak will empty the tank in x hrs
Then, 1/9 - 1/x = 1/13
x = 29.25 hrs
Correct Answer: 3 3/5
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