An audio signal consists of two distinct sound. One a human speech signal in the frequency band of `200Hz` to `2700Hz`, while the other is a high frequency music signal in the frequency band of `10200Hz` to `15200Hz`. The ratio of the AM signal together to the AM signal band width required to send just the human speech is:

Options

A. `6`
B. `5`
C. `3`
D. none of these

Explanation

To solve the problem, we need to determine the bandwidths of the audio signals and then find the ratio of the AM signal bandwidth required to send both signals to the AM signal bandwidth required to send just the human speech.

### Step-by-Step Solution:

1. **Determine the Bandwidth of Human Speech:**
- The frequency range for human speech is given as 200 Hz to 2700 Hz.
- Bandwidth (FH) = Upper Frequency - Lower Frequency
- FH = 2700 Hz - 200 Hz = 2500 Hz

2. **Determine the Bandwidth of Music Signal:**
- The frequency range for the music signal is given as 10200 Hz to 15200 Hz.
- Bandwidth (FM) = Upper Frequency - Lower Frequency
- FM = 15200 Hz - 10200 Hz = 5000 Hz

3. **Calculate the AM Signal Bandwidth for Human Speech:**
- The AM signal bandwidth required to send the human speech signal (BH) is twice the bandwidth of the human speech.
- BH = 2 * FH = 2 * 2500 Hz = 5000 Hz

4. **Calculate the AM Signal Bandwidth for Both Signals:**
- The AM signal bandwidth required to send both the human speech and music signals (BM) is given by:
- BM = 2 * FM + BH
- BM = 2 * 5000 Hz + 5000 Hz = 10000 Hz + 5000 Hz = 15000 Hz

5. **Calculate the Ratio of the AM Signal Bandwidths:**
- We need to find the ratio of the AM signal bandwidth for both signals (BM) to the AM signal bandwidth for just the human speech (BH).
- Ratio = BM / BH = 15000 Hz / 5000 Hz = 3

Thus, the ratio of the AM signal bandwidth required to send both signals to the AM signal bandwidth required to send just the human speech is **3:1**.

### Final Answer:
The ratio is **3:1**.