Answer:
The answer is 20.865 [ 21 sec approximately ]
Step-by-step explanation:
Given data
A chocolate fudge machine uses 4 different nozzles to make a glass of fudge A for vanilla ice-cream, B for chocolate ice-cream, C for fruits and nuts and D for fresh crèam
A can fill the glass in 30 sec; B can fill the glass in 40 sec
C can fill the glass in 20 sec; D can fill the glass in 10 sec
To fill a glass the machine opens each nozzle one by one for a second
in the sequence A B C D A B C D A B C D...
Here we need to find in how many seconds the machine can make a chocolate fudge ?
As per the given sequence
For 1st sec A nozzle can fill [tex]\frac{1}{30}[/tex] of the glass
For 2nd sec B nozzle can fill [tex]\frac{1}{40}[/tex] of the glass
For 3rd sec C nozzle can fill [tex]\frac{1}{20}[/tex] of the glass
For 4th sec D nozzle can fill [tex]\frac{1}{10}[/tex] of the glass
Therefore,
for 4 sec the part of the glass can be filled = [tex]\frac{1}{30} +\frac{1}{40} + \frac{1}{20} + \frac{1}{10}[/tex]
= [tex]\frac{4+3+6+10}{120} = \frac{23}{120}[/tex]
In 4 sec [tex]\frac{23}{120}[/tex] of the glass can be filled
Therefore, time taken to fill 1 glass = [tex]\frac{120}{23} (4)= \frac{388}{23} = 20.865[/tex] sec
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