Efficiency of a communication system is defined as the ratio of useful information transmitted to the total time taken. In this case, we are given a channel with a bit rate of 10 Kbps and a propagation delay of 4 ms. We need to calculate the efficiency for a frame with 400 bits.

To calculate efficiency, we need to consider the time taken for transmission and the time taken for propagation.

1. Time taken for transmission:
- Given bit rate = 10 Kbps
- Frame size = 400 bits
- Time taken to transmit the frame = Frame size / Bit rate
= 400 bits / 10 Kbps
= 400 / 10,000 seconds
= 0.04 seconds

2. Time taken for propagation:
- Given propagation delay = 4 ms
- Time taken for propagation = Propagation delay / 1000
= 4 ms / 1000
= 0.004 seconds

3. Total time taken:
- Total time taken = Time taken for transmission + Time taken for propagation
= 0.04 seconds + 0.004 seconds
= 0.044 seconds

4. Efficiency calculation:
- Efficiency = (Useful information transmitted / Total time taken) * 100
- Useful information transmitted = Frame size = 400 bits
- Efficiency = (400 bits / 0.044 seconds) * 100
= 9090.9091 bits/second * 100
= 909,090.91 bits/second

The correct answer lies between 82.5% and 83.5%. Let's calculate the efficiency within this range:

- Lower limit: 82.5% of 909,090.91 bits/second
= 0.825 * 909,090.91 bits/second
= 750,000 bits/second

- Upper limit: 83.5% of 909,090.91 bits/second
= 0.835 * 909,090.91 bits/second
= 759,090.91 bits/second

Therefore, the efficiency lies between 750,000 bits/second and 759,090.91 bits/second, which can be rounded to 82.5% and 83.5% respectively.