In the flowchart, each rectangular box represents a distinct stage in

I have a doubt, would we not be taking into account the batches moving in parallel that is while 1/4 of the batch would be re heated (taking additional 20 mins) the rest of the batch would move to next stage

What effect this would create would be that during the movement of rest of batch would be covered in the re heating times
I.e while 1/4 of batch would be getting re heated, the rest of the batch would have finished with HCL mixing

shauryahanda


The processing time for a single batch will stop when it has finished the Drying stage. So, even if there are some batches in the earlier stages, the average time required will not change.

ptkm great explanation. Why are we only take care of 1/4 and not 2/4 as it has total 3/4?
Could you help clarify? Thanks

The calculations of this question was hard. It required concepts of Sets, Weighted Average and LCM. Make the denominator of all fractions to be 12 (LCM of 4 and 3 for easy calculation)

- Two twelfth of the set require ONLY additional heating
- One twelfth of the set require BOTH additional heating and additional HCl mixing
- Five twelfth of the set require ONLY additional HCl mixing
- Four twelfth of the set require NOTHING at all.

Now, use weighted average's concept to solve question 1 and 2. If you require detailed solution, mention me and I will add it here.­

­my solution in the picture attached!

 

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If we don't get caught up into the traps of calculations and quarter of something and half of something else  , this one is a fairly straightforward question if followed in a logical manner.

Let's assume that a batch consists of 4 units of specialty chemical (Doesn't matter if that adds up to 50 kilograms or some other number).

BUT WHY 4 UNITS? Cause the information mentions that 3/4th of the batch passes through without additional heating and 1/2 of the batch requires additional HCL mixing. So to avoid getting caught up in 3/4th of 50 kilograms and deal with decimals or fractions, We can just assume 4 units in a batch.

Now that it is clear, let's proceed with the question.

First, if all the units (4 of them) in a batch pass through the processes without needing anything additional (no additional heating, no additional HCL mixing), then the time required is:

• Heating at 200K: 30 mins
• Sifting: 5 mins
• HCL mixing: 20 mins
• Filtration: 10 mins
• Drying at 150K: 60 mins

Total time: 125 mins for each unit.

Hence, the average time is 125 mins.
But
1 unit (3/4th of the batch) requires additional heating. So it adds 20 mins to the process.
And
2 units (1/2 of the batch) require additional HCL mixing. So, it adds 20 + 20 mins to the process.

So, an additional 60 mins are required. Hence, an average of 60/4 = 15 mins are to be added to the 125 mins average time.

Thus, the average time for the process is 140 mins. The visual representation of the same is given below.



Now, we can apply the exact same process to answer the second question.

Every unit must pass through:

• Heating at 200K
• Sifting
• HCL mixing
• Filtration
• Drying at 150K

So, average number of stages is 5.

But
1 unit (3/4th of the batch) requires additional heating. So it adds 1 more stage to the process.
And
2 units (1/2 of the batch) require additional HCL mixing. So, it adds 2 more stages to the process.

So, an additional 3 stages are required. Hence, an average of 3/4 = 0.75 stages are to be added to the 5 stages.

Thus, the average number of stages for the process is 5.75. The visual representation of the same is given below.

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