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

 
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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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