Robert Bosch Pipes and Cistern Quiz-4

Solution: Part filled by Pipe P1 in 1 hour = 1/7
Part filled by Pipe P2 in 1 hour = 1/8
Pipe P3 can empty the pool in 12 hours.
Therefore, part emptied by pipe P3 in 1 hour =1/12

Total part filled by Pipe P1, P2, and P3 together in 1 hour = 1/7 + 1/8 – 1/12 = 31/168
So, the pool can be filled in 168/31 hours.

Solution:
Let the size of the container be = 60 units [LCM (20, 30)]
Efficiency of pipe P1 = 60 / 20 = 3 units
Efficiency of pipe P2 = 60 / 30 = 2 units
Combined efficiency of pipe P1 and pipe P2 = 5 units/min
So, time required to empty the container with both pipes = 60 / 5 = 12 mins

Solution:
Water tank filled in 6 hours = 1/6
Now, due to outlet pipe, 1 hour part filled = 1/8
Part of the water tank unfilled in 1 hour = 1/6 - 1/8 = 1/24
So, the leak will empty the full water tank in 24 hrs

Solution:
Let the time taken by pipe P alone is x.
Then pipe Q and R will take x2 and x4
Therefore, 1/x + 2/x + 4/x = 1/6
= 7/x = 1/6
Thus, x = 42 hours

Solution:
Part Pipe A can fill in 1 hour = 1/7
Part Pipe B can fill in 1 hour = 1/8
Pipe C can empty the tank in 10 hours.
Therefore, amount emptied by Pipe C in 1 hour =1/10

Total part filled by Pipe A, B, and C together in 1 hour = 1/7 + 1/8 – 1/10 = 1/14
So, the tank can be filled in 14 hours.

Solution:
Let the time taken by slower pipe be x.
Then, faster pipe will take time x / 4
Therefore, 1/x + 4/x = 1/40
= 5/x = 1 / 40
= x = 200 minutes.

Solution:
Cistern filled by both C and D in 1 minute = 1/30 + 1/20 = 1/12
If we assume the cistern to be filled in x minutes
Then, x/2(1/12 + 1/20) = 1
= x/2 * 2/15 = 1
= x= 15 minutes

Solution:
Given, time taken by a tap to completely fill the cistern = 4 hours
Therefore, time taken a tap to fill the cistern half = 2 hours (4/2)
Cistern filled by three pipes in 1 hour = 3*1/4 = 3/4 hours.
Therefore, remaining part = 1-1/2 = ½
= 3/4 : ½ = 1 : x
x = 2/3 = 40 minutes.
Hence, total time taken = 2 hours and 40 minutes.

Solution:
Cistern filled in 3 hours = 3/9 = 1/3
Then remaining part will be 2/3
Given, pipe1 and pipe2 can fill the 2/3 cistern in 9 hours.
Therefore, pipe1 and pipe2 1 hour work = 2/3*1/9 = 2/27
Then pipe3’s 1 hour work = 1/9 - 2/27 = 1/27
Thus, pipe3 will take 27 hours to fill the cistern alone.

Solution:
If pipe x takes 3 minutes to fill the tub
Then the tub filled by pipe X in 1 minute = 1/3
If pipe Y takes 9 minutes to fill the tub
Then the tub filled by pipe Y in 1 minute = 1/9
Together they can fill in 1 minute = 1/3 + 1/9 = 4/9
Therefore, together pipe X and Y can fill tub in 9/4 minutes
Thus, 9/4 =2 14 minutes = 2 minutes 20 seconds.