Pipes and Cistern- Aptitude Questions and Answers

Three Pipes A,B and C together filled a tank in 6 hours
So 1 hour work of A,B and C =1/6
C closed after 2 hour's, Part filled in 2 hours working together(A,B and C) = 2/6 = 1/3
Remaining part = (1-1/3) = 2/3

A and B can fill remaining in 8 hours, (A + B)'s 8 hour's work = 2/3

So, (A+B)'s 1 hour work = 2/24=1/12

Therefore C's 1 hour's work
= [(A+B+C)'s 1 hour]-[(A+B)'s 1 hr work]
=(1/6 - 1/12) = 1/12

C alone can fill the tank in 12 hours

As the pipes are operating alternatively for one minute, thus (A+B)'s 2 minutes job is =(1/4 +1/6) =5/12
in next, 2 minutes both pipe can fill another 5/12 part.
So in 4 minutes A and B are operating alternatively will fill 5/12 + 5/12 = 5/6

Remaining part of cistern= 1 - 5/6 =1/6

Pipe A can fill 1/4 part of the cistern in 1 minute,and can fill 1/6 part of the cistern in = 4*(1/6) =2/3 minutes

Total time taken to fill the Cistern = time taken to fill (5/6 part + 1/6 part)
=> 4 minutes + 2/3 minutes = 4(2/3) minutes Or, 4 minutes 40 seconds

If a pipe can fill a tank in x hours, then : part filled in 1 hour = 1/x

Part filled A in 1 hr= (1/45)
Part filled B in 1 hr= (1/36)
Part filled by (A+B) together in 1 hr=(1/45)+(1/36)=1/20

So, The tank will be full in 20 hr.

If a pipe can fill a tank in x hours, then : part filled in 1 hour = 1/x

Then,when a pipe fills a tank in 6 h, then the part of tank filled in 1 h = 1/6
Hence ,required part of the tank to be filled in 1h = 1/6 part

If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours (where x > y), then on opening both the pipes, the net part emptied in 1 hour = (1/y)-(1/x)

= (1/8 - 1/16) = 1/16
Time taken to empty the full tank = 16 min.
Hence, time taken to empty the half tank = 8 min

If a pipe can .fill a tank in x hours and another pipe can empty the full tank in y hours (where y> x), then on opening both the pipes, the net part filled in 1 hour = (1/x)-(1/y)

= (1/2 - 1/3) = 1/6
Hence, time taken to fill the cistern = 6 hours

44 pipes => 27 hours
66 pipes=> ?

Amount of work done is same for filling a pipe, So
44*27 = 66*X
X = 44*27 / 66
X = 18
66 pipes can fill one tanks in 18 hours.
they will fill 4 tanks in 18*4 = 72 hours