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41. Three taps A, B, C can fill an overhead tank in 4, 6 and 12 hours respectively. How long would the three taps take to fill the tank if all of them are opened together ?
(A + B + C)'s efficiency
= 3 + 2 + 1
= 6 units/hr
(A + B + C) can fill the tank in
Solution:
(A + B + C)'s efficiency
= 3 + 2 + 1
= 6 units/hr
(A + B + C) can fill the tank in
42. Having the same capacity 9 taps fill up a water tank in 20 minutes. How many taps of the same capacity are required to fill up the same water tank in 15 minutes ?
Solution:
43. Pipe A can fill a tank in 4 hours and pipe B can fill it 6 hours. If they are opened on alternate hours and if pipe A is opened first then in how many hours, the tank shall be full ?
B → 6 hours
According to question,
⇒ For the first hour tap A is opened and B for second hour
⇒ Work done by both in 2 hours
⇒ Remaining part
= 12 - 10 = 2 liters
⇒ Again 5th hour A will be opened Tap A will fill the 2 liters water with its efficiency = hours
⇒ Therefore tank will be filled in
= hours
= hours
Solution:
A → 4 hoursB → 6 hours
According to question,
⇒ For the first hour tap A is opened and B for second hour
⇒ Work done by both in 2 hours
⇒ Remaining part
= 12 - 10 = 2 liters
⇒ Again 5th hour A will be opened Tap A will fill the 2 liters water with its efficiency = hours
⇒ Therefore tank will be filled in
= hours
= hours
44. Pipe A can fill the tank in 8 hours and pipe B can fill it in 12 hours. If pipe A is opened at 7:00 AM and pipe B is opened at 9:00 AM, then at what time will the tank be full ?
A opened 2 hours early to B
In 2 hours A can do 3 × 2 = 6 unit work
Remaining work = 24 - 6 = 18
A + B can do it in
∴ Tank will be full in 9 AM + 3 hours 36 minutes = 12.36 PM
Solution:
A opened 2 hours early to B
In 2 hours A can do 3 × 2 = 6 unit work
Remaining work = 24 - 6 = 18
A + B can do it in
∴ Tank will be full in 9 AM + 3 hours 36 minutes = 12.36 PM
45. Two pipes A and B can fill a tank with water in 30 minutes and 45 minutes respectively. The third pipe C can empty the tank in 36 minutes. First A and B are opened. After 12 minutes C is opened. Total time ( in minutes ) in which the tank will be filled up is -
A . . . . . (+) 30 minutes
B . . . . . (+) 45 minutes
C . . . . . (-) 36 minutes
⇒ Water filled by (A + B) in 12 min
= 12 × (6 + 4)
= 12 × 10 = 120 liters
⇒ Remaining capacity
= 180 - 120 = 60 liters
⇒ After 12 minutes emptied pipe C is also opened
⇒ Total capacity (A + B - C)
= (6 + 4 - 5) = 5 liters/minutes
⇒ Time taken by (A + B - C) with capacity 5 liters/minutes to fill the remaining part
⇒ Therefore, total time in which the tank will be filled up is
= 12 + 12
= 24 minutes
Solution:
A . . . . . (+) 30 minutes
B . . . . . (+) 45 minutes
C . . . . . (-) 36 minutes
⇒ Water filled by (A + B) in 12 min
= 12 × (6 + 4)
= 12 × 10 = 120 liters
⇒ Remaining capacity
= 180 - 120 = 60 liters
⇒ After 12 minutes emptied pipe C is also opened
⇒ Total capacity (A + B - C)
= (6 + 4 - 5) = 5 liters/minutes
⇒ Time taken by (A + B - C) with capacity 5 liters/minutes to fill the remaining part
⇒ Therefore, total time in which the tank will be filled up is
= 12 + 12
= 24 minutes
46. Three pipes A, B and C can fill a tank in 6 hours, 9 hours and 12 hours respectively. B and C are opened for half an hour, then A is also opened. The time taken by the three pipes together to fill the remaining part of the tank is -
In half an hour (B + C) must have filled
Capacity left
Now all pipes will fill the remaining tank
Solution:
In half an hour (B + C) must have filled
Capacity left
Now all pipes will fill the remaining tank
47. A tap drips at a rate of one drop/second. 600 drops make 100 ml. The number of liters wasted in 300 days is -
Solution:
48. Pipes A and B can fill a tank in 12 minutes and 15 minutes, respectively. The tank when fill can be emptied by pipe C in x minutes. When all the three pipes are opened simultaneously, the tank is full in 10 minutes. The value of x is:
No explanation ¯\_(ツ)_/¯
49. A tap can fill a tank in hours. Because of a leak, it took hours to fill the tank. In how much time (in hours) will the leak alone empty 30% of the tank?
No explanation ¯\_(ツ)_/¯
50. Two pipes A and B can fill a tank in 12 minutes and 24 minutes, respectively, while a third pipe C can empty the full tank in 32 minutes. All the three pipes are opened simultaneously. How-ever, pipe C is closed 2 minutes before the tank is filled. In how much time (in minutes) will the tank be full?
No explanation ¯\_(ツ)_/¯