(A):Average speed is equal to total distance travelled divided by total time taken .
(R ):The average speed of an object may be equal to arithmetic mean of individual speed

Answer

To analyze the statements provided in the question, we will break down the concepts of average speed and its relationship with individual speeds.

### Step-by-Step Solution:

1. **Understanding Average Speed**:
- The average speed of an object is defined as the total distance traveled divided by the total time taken.
- Mathematically, it can be expressed as:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]
- This statement (A) is true.

2. **Understanding Individual Speeds**:
- The average speed can also be related to individual speeds when the object travels at different speeds for equal intervals of time.
- If an object travels at speeds \(v_1\), \(v_2\), and \(v_3\) for equal time intervals \(t_0\), the total distance traveled can be expressed as:
\[ \text{Total Distance} = v_1 \cdot t_0 + v_2 \cdot t_0 + v_3 \cdot t_0 = t_0(v_1 + v_2 + v_3) \]
- The total time taken is:
\[ \text{Total Time} = 3t_0 \]

3. **Calculating Average Speed with Individual Speeds**:
- Now, substituting these into the average speed formula:
\[ \text{Average Speed} = \frac{t_0(v_1 + v_2 + v_3)}{3t_0} = \frac{v_1 + v_2 + v_3}{3} \]
- This shows that the average speed can indeed be the arithmetic mean of the individual speeds \(v_1\), \(v_2\), and \(v_3\) when the time intervals are equal.

4. **Conclusion**:
- Statement (A) is true as per the definition of average speed.
- Statement (R) is also true, but it is conditional. It is true only under the specific condition that the object travels at different speeds for equal time intervals.
- Therefore, both statements are true, but (R) does not universally explain (A).

### Final Answer:
- Both statements (A) and (R) are true, but (R) is not the correct explanation for (A).