Similar type here: https://gateoverflow.in/191569/gateforum-pure-aloha-numerical

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Let cluster of stations share 48kbps of pure aloha channel. Every station outputs frame of length 1024 bit in every 50 seconds. Then what is the maximum value of number of stations?

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Since its pure aloha. So max Bandwidth utilization is 18% of 48Kbps.

And its given, Each station transmits

1024 bits in 50 seconds

$\therefore$ In 1 second --- $\frac{1024}{50}$ bits

Let's say there are N stations.

So N*$\frac{1024}{50}$=18% of 48*1000

N=$\left \lfloor 421.875 \right \rfloor$

$\therefore$ N=421

And its given, Each station transmits

1024 bits in 50 seconds

$\therefore$ In 1 second --- $\frac{1024}{50}$ bits

Let's say there are N stations.

So N*$\frac{1024}{50}$=18% of 48*1000

N=$\left \lfloor 421.875 \right \rfloor$

$\therefore$ N=421

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