Dhruv, would you mind posting what you have done so far about this? We aren't here to provide ready-made solutions, you know 😀

Well, I guess you start of with modulating the signal (PCM), add repeaters/amplifiers, etc.

One of the many ways that I can think of -

1) As suggested, use 8-bit PCM at 8kHz sampling (data rate is 64kbps). It is good enough for voice.
2) FM modulate all 10 PCM signals with 10 different carriers equally spaced in the 500KHz band. This is FDM transmission.
3) The advantage I see with FM is that signal level is not a very important criterion. As long as the frequency deviation is there you can still retrieve digital data. Nevertheless I feel repeaters would be required because 100dB looks like a big loss. You may also decide the need for repeaters based on the demodulator sensitivity.

Note these points -
I view this problem in a way that it is not important to find a solution (in this case many are possible). I think the aim here is to test your understanding of various transmission techniques, based on which you need to design a simple system, with as little components as possible and with as low power consumption as possible. I am not sure if you need to consider the cost aspect here, but I feel you can leave it.
So before you jump into a solution, try to spend some time on vaguely designing using other techniques (some 3-4 others you know) that you have learnt and try to choose the simplest and most effective one.

So the above mentioned solution may not be the best. So think in similar lines about other possibilities.
All the best.
Karthik
😁

^ adding to reachrkata's point for a simple system, at least you dont have to worry about drawing complicated waveforms 😉

1 dB per km is a huge loss. Considering that every 3dB loss accounts for power dropping to half it's initial value. 100 km leads to halving of power 33 times and the final power limit has to at least 1 mW! Taking a margin of 1.5 the initial signal strength therefore has to be at least (1.5 * 2^(33-1)) = 6.5MW approx.

That's awesome... or am I going terribly wrong somewhere?

Well, no matter what be the modulation technique adopted this high loss won't work. Repeaters have to be used, no doubt.

Well Dhruv. Read Kennedy. You don't have to be lazy. This sounds like a very complicated problem but there are many ways you can answer it in simple ways. Just get your basics right. There is no right or wrong answer to this problem as I understand it. It's just for academic purpose and is intended only to test your grasp of the subject. And here I see, my view coincide with that of Karthik. I second him.