Step 1: Concept
The Suladi Sapta Tala system consists of seven basic talas. Their total duration (Aksharas) is determined by their unique structural components (angas) and the chosen Jaati (which defines the length of the Laghu).
Step 2: Structural and Beat Calculation
1. Matya Tala has the structural formula: Laghu - Drutam - Laghu ($L \ D \ L$).
- For Statement (a) [Chatusra Jati, $L_4$]:
$$\text{Total Beats} = L_4 + D_2 + L_4 = 4 + 2 + 4 = 10 \text{ Aksharas.}$$
This statement is Correct.
- For Statement (b) [Tisra Jati, $L_3$]:
$$\text{Total Beats} = L_3 + D_2 + L_3 = 3 + 2 + 3 = 8 \text{ Aksharas.}$$
The statement says 20 Aksharas, which is Incorrect.
2. Ata Tala has the structural formula: Laghu - Laghu - Drutam - Drutam ($L \ L \ D \ D$).
- For Statement (c) [Khanda Jati, $L_5$]:
$$\text{Total Beats} = L_5 + L_5 + D_2 + D_2 = 5 + 5 + 2 + 2 = 14 \text{ Aksharas.}$$
This statement is Correct.
3. Triputa Tala has the structural formula: Laghu - Drutam - Drutam ($L \ D \ D$).
- For Statement (d) [Tisra Jati, $L_3$]:
$$\text{Total Beats} = L_3 + D_2 + D_2 = 3 + 2 + 2 = 7 \text{ Aksharas.}$$
The statement says 6 Aksharas, which is Incorrect.
Step 3: Conclusion
Statements (a) and (c) are correct, which corresponds to option (A).
Final Answer: (A)