This beaker is of no use

Algebra Level pending

I have beaker of height 16cm, which has three holes on its curved sufrace area as shown in the figure. Adjacent holes are at a uniform distance of 4cm from each other. The lowest hole is 4cm above the bottom of the beaker and the topmost hole is 4cm below the rim of the beaker.

A pipe fills the beaker with water in 4 hours with the condition that all the holes are closed. All the holes have the same efficiency and each one of them can empty the beaker in 72 hours, if they were at the bottom of the beaker.

Now this Question has some rules, which are as follows:

  • When the water level reaches the first hole, the hole empties the beaker with the efficiency of 72 hours.
  • As soon as the water level reaches the second hole, the efficiency of the bottom most hole doubles (36 hours), where as the second hole will have the efficiency of emptying the beaker in 72 hours at that time.
  • As soon as water level reaches the topmost hole, the second holes efficiency doubles (36 hours) and the bottom most hole efficiency gets 4 times(18 hours) whereas the efficiency of topmost hole for emptying the beaker is 72 hours.

How much time will the pipe take, to fill the beaker with all the holes open? Give your answers in hours by correcting it to three decimal places.

Assumptions and Caveats:When I talk about efficiency of a hole it relates to how much time the hole will take to empty the beaker. An example to enter the answer could be, if you are getting an answer like 4 hours 45 minutes, enter it as 4.75. Another example can be , if you are getting an answer like 4 and a half hours, enter your answer as 4.5. The holes and the pipe work according to the mentioned rules.


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