A

Step 1: Identify the forces acting on the masses in the system. We have three masses:

• m₁ = 10 kg
  
• m₂ = 20 kg
  
• m₃ = 30 kg
  

The total external force acting on the system is 60 N.

Step 2: Calculate the total mass of the system.
Total mass = m₁ + m₂ + m₃
Total mass = 10 kg + 20 kg + 30 kg = 60 kg.

Step 3: Calculate the acceleration of the system using Newton's second law:
F = ma
Therefore, a = \frac{F}{m} = \frac{60 ext{ N}}{60 ext{ kg}} = 1 ext{ m/s}^2.

Step 4: Analyze the forces on each mass to find tensions T₁ and T₂.
For m₃ (30 kg):
\( F_{net} = m_3 imes a \)
\( T_2 = m_3 imes a \)
\( T_2 = 30 ext{ kg} imes 1 ext{ m/s}^2 = 30 ext{ N} \)

For m₂ (20 kg):
The tension T₁ and T₂ acting on m₂ gives:
\( T_1 - T_2 = m_2 imes a \)
\( T_1 - 30 = 20 ext{ kg} imes 1 ext{ m/s}^2 \)
\( T_1 - 30 = 20 \)
\( T_1 = 50 ext{ N} \)

For m₁ (10 kg):
\( T_1 = m_1 imes a \)
\( T_1 = 10 ext{ kg} imes 1 ext{ m/s}^2 = 10 ext{ N} \)

Therefore, T₁ = 10 N and T₂ = 30 N.
Therefore, the answer is option A: 10, 30.