Pipes and Cistern
- A pipe can empty a tank in 40 minutes. A second pipe with diameter twice as much as that of the first is also attached with the tank to empty it. The two together can empty the tank in :
-
View Hint View Answer Discuss in Forum
As per the given in question ,
Here, the diameter of the second pipe is twice that of first pipe.
∴ Volume of water emptied by the second pipe will be 4 times to that of first pipe.
Hence, time taken will be 1/4 of the first pipe.∴ Second pipe will empty the tank in 1 × 40 = 10 minutes 4
When both the pipes are open, the part of the tank emptied in1 minute = 1 + 1 = 1 + 4 = 1 40 10 40 8
Correct Option: A
As per the given in question ,
Here, the diameter of the second pipe is twice that of first pipe.
∴ Volume of water emptied by the second pipe will be 4 times to that of first pipe.
Hence, time taken will be 1/4 of the first pipe.∴ Second pipe will empty the tank in 1 × 40 = 10 minutes 4
When both the pipes are open, the part of the tank emptied in1 minute = 1 + 1 = 1 + 4 = 1 40 10 40 8
Hence, the tank will be emptied in 8 minutes.
- Two pipes can fill a tank with water in 15 and 12 hours respectively and a third pipe can empty it in 4 hours. If the pipes be opened in order at 8, 9 and 11 a.m. respectively, the tank will be emptied at
-
View Hint View Answer Discuss in Forum
On the basis of given details in question ,
Part filled by A from 8 a.m to 11 a.m. = 3 = 1 15 5 Part filled by B from 9 a.m. to 11 a.m. = 2 = 1 12 6 Total Part filled till 11 a.m. = 1 + 1 = 6 + 5 = 11 5 6 30 30
At 11 a.m. pipe C is opened to empty it.∴ Part of tank emptied in 1 hour = 1 - 1 - 1 4 15 12 Part of tank emptied in 1 hour = 15 - 4 - 5 = 1 60 10
Correct Option: A
On the basis of given details in question ,
Part filled by A from 8 a.m to 11 a.m. = 3 = 1 15 5 Part filled by B from 9 a.m. to 11 a.m. = 2 = 1 12 6 Total Part filled till 11 a.m. = 1 + 1 = 6 + 5 = 11 5 6 30 30
At 11 a.m. pipe C is opened to empty it.∴ Part of tank emptied in 1 hour = 1 - 1 - 1 4 15 12 Part of tank emptied in 1 hour = 15 - 4 - 5 = 1 60 10 ∴ 11 part will be emptied in 11 × 10 = 11 hours or 3 2 30 30 3 3
i.e. 3 hours 40 minutes or at 11 : 40 a.m.
Therefore , the tank will be emptied at 11 : 40 a.m.
- A Boy and girl together fill a cistern with water. The boy pours 4 litres of water every 3 minutes and the girl pours 3 litres every 4 minutes. How much time will it take to fill 100 litres of water in the cistern ?
-
View Hint View Answer Discuss in Forum
On the basis of given details in question ,
Water filled by the boy in 1 minute = 4 3 Water filled by a girl in 1 minute = 3 4 Water filled by the boy and girl in 1 minute = 4 + 3 = 16 + 9 = 25 litres 3 4 12 12
Correct Option: C
On the basis of given details in question ,
Water filled by the boy in 1 minute = 4 3 Water filled by a girl in 1 minute = 3 4 Water filled by the boy and girl in 1 minute = 4 + 3 = 16 + 9 = 25 litres 3 4 12 12 ∴ Time taken to fill 100 litres = 100 × 12 = 48 minutes 25
- A pipe of diameter d can drain a certain water tank in 40 minutes. The time taken by a pipe of diameter 2d for doing the same job in :
-
View Hint View Answer Discuss in Forum
As we know that ,
Time α 1 cross sectional area of the pipe Time α 1 π d² 4 Time α 1 d² ∴ t2 = (d1)² t1 (d2)²
[Being inversely related]t2 = t1 
d1 
² d2
t1 = 40 minutes, d1 = d, d2 = 2d
Correct Option: B
As we know that ,
Time α 1 cross sectional area of the pipe Time α 1 π d² 4 Time α 1 d² ∴ t2 = (d1)² t1 (d2)²
[Being inversely related]t2 = t1 d1 ² d2
t1 = 40 minutes, d1 = d, d2 = 2d∴t2 = 40 d ² 2d t2 = 40 1 ² 2
Hence , t2 = 10 minutes
- Two pipes A and B can fill a water tank in 20 and 24 minutes respectively and a third pipe C can empty at the rate of 3 gallons per minute. If A, B and C are opened together to fill the tank in 15 minutes, the capacity (in gallons) of the tank is :
-
View Hint View Answer Discuss in Forum
Let the capacity of the tank be q gallons.
When all the pipes A, B and C are opened simultaneouslyQuantity of water filled in the tank in 1 minute = q + q - 3 20 24
According to the question ,q + q - 3 = q 20 24 15 ⇒ q + q - q = 3 20 24 15
Correct Option: C
Let the capacity of the tank be q gallons.
When all the pipes A, B and C are opened simultaneouslyQuantity of water filled in the tank in 1 minute = q + q - 3 20 24
According to the question ,q + q - 3 = q 20 24 15 ⇒ q + q - q = 3 20 24 15 ⇒ 6q + 5q - 8q = 3 120
⇒ 3 q = 3 × 120⇒ q = 3 × 120 = 120 gallons 3
