Since 5 Roberts can manufacture 5 cups in 5 seconds.
It must be that 25 Roberts should be able to manufacture 5 cups in 1 second.
Because as Roberts increase time taken to manufacture same number of cups decreases.
However we are required to find the time taken for 25 cups which is 5 times the original amount therefore it will take 5*1 sec = 5 seconds.

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Think of it this was.
it takes 5 machines 5 second to make 5 cups, so their individual work rate must be 1 cup/5 sec (work= rate*time)
now they asked how much time will 25 robot take for 25 cups. we know the each robot makes 1 cup/5 sec. so it should take them 5 sec to make 25 cups.