**Solution:**

**Given:**
- Horizontal force applied: 300 Newton
- Mass of block 1 (m₁): 10 kg
- Mass of block 2 (M₂): 20 kg
- Light and inextensible string connecting the two blocks
- Horizontal frictionless surface

**To find:**
- Acceleration of each mass (m₁ and M₂)

**Assumptions:**
- The string connecting the blocks is light and inextensible, meaning its mass is negligible and it does not stretch or break.
- The pulley or any other device is frictionless.
- There are no external forces acting on the system other than the applied force.

**Approach:**
To find the acceleration of each mass, we need to analyze the forces acting on each block and apply Newton's second law of motion (F = ma).

**For block 1 (m₁):**
1. Tension in the string: The tension in the string will be the force applied by block 2 on the string, which will be equal to the force applied by block 1 on the string (Newton's third law). Let's denote this tension as T.
2. Net force: The net force acting on block 1 is the difference between the applied force and the tension force.
- Net force on block 1 = Applied force - T
- Net force on block 1 = 300 N - T
3. Using Newton's second law of motion, we have:
- Net force on block 1 = mass of block 1 * acceleration of block 1
- 300 N - T = 10 kg * acceleration of block 1

**For block 2 (M₂):**
1. Tension in the string: The tension in the string will be the force applied by block 2 on the string, which will be equal to the force applied by block 1 on the string (Newton's third law). Let's denote this tension as T.
2. Net force: The net force acting on block 2 is the sum of the tension force and the applied force.
- Net force on block 2 = T + Applied force
- Net force on block 2 = T + 300 N
3. Using Newton's second law of motion, we have:
- Net force on block 2 = mass of block 2 * acceleration of block 2
- T + 300 N = 20 kg * acceleration of block 2

**Solving the equations:**
We have two equations based on Newton's second law for each block. We can solve these equations simultaneously to find the acceleration of each block.

1. 300 N - T = 10 kg * acceleration of block 1
2. T + 300 N = 20 kg * acceleration of block 2

We can solve these equations to find the values of T, acceleration of block 1, and acceleration of block 2.