**Explanation:**

To solve this problem, we need to understand the concept of work done by friction and how it relates to the coefficient of friction.

**Work done by friction:**
When an object moves along a rough surface, the force of friction opposes its motion. The work done by friction is given by the equation:

**Work = force of friction x distance**

If the net work done by friction on the system is zero, it means that the work done by friction on the 10 kg block is equal in magnitude and opposite in direction to the work done by friction on the 5 kg block. This can only happen if the coefficient of friction between the two blocks is the same.

Let's calculate the work done by friction on both blocks separately.

**Work done by friction on the 10 kg block:**
The force applied on the 10 kg block is 30 N. Since the net work done by friction on the system is zero, the work done by friction on the 10 kg block must be equal in magnitude and opposite in direction to the applied force.

Let's assume the coefficient of friction between the 10 kg block and the ground is μ1. The normal force on the 10 kg block is equal to its weight, which is given by:

**Normal force = mass x gravity = 10 kg x 9.8 m/s^2 = 98 N**

The frictional force on the 10 kg block is given by:

**Frictional force = coefficient of friction x normal force = μ1 x 98 N**

The work done by friction on the 10 kg block is equal to the force of friction multiplied by the distance traveled by the block. Let's assume the distance traveled by the block is d.

**Work done by friction on the 10 kg block = μ1 x 98 N x d**

**Work done by the applied force on the 10 kg block = 30 N x d**

Since the net work done by friction on the system is zero, we can equate the work done by friction to the work done by the applied force:

**μ1 x 98 N x d = 30 N x d**

Simplifying the equation, we find:

**μ1 = 30 N / 98 N = 0.3061**

Therefore, the coefficient of friction between the 10 kg block and the ground is approximately 0.3061.

**Work done by friction on the 5 kg block:**
Since the coefficient of friction between the 10 kg block and the 5 kg block is the same as the coefficient of friction between the 10 kg block and the ground, the work done by friction on the 5 kg block can be calculated using the same formula:

**Work done by friction on the 5 kg block = μ1 x normal force on the 5 kg block x distance**

The normal force on the 5 kg block is equal to its weight, which is given by:

**Normal force = mass x gravity = 5 kg x 9.8 m/s^2 = 49 N**

Therefore, the work done by friction on the 5 kg block is:

**Work done by friction on the 5 kg block = μ1 x 49 N x distance**

Since the net work done by friction on the system is zero, the work done by the applied force on the 5 kg block must be equal in magnitude and opposite

0.1 and 0.3