**Solution:**

Given data:
- Thickness of the top layer (clay) = 5 m
- Shear strength of the top clay layer = 45 kN/m2
- Shear strength of the bottom layer = 100 kN/m2
- Safe load required = 380 kN
- Factor of safety = 2.0

To determine the length of the bored pile required to carry the safe load of 380 kN, we need to consider the shear strength of both the top and bottom layers of the cohesive soil.

**Step 1: Calculate the ultimate bearing capacity of the soil**

The ultimate bearing capacity of the soil can be calculated using the following formula:

$Q_u = cN_c + qN_q + 0.5γBN_γ$

Where:
- $Q_u$ = Ultimate bearing capacity of the soil
- $c$ = Cohesion of the soil
- $N_c, N_q, N_γ$ = Bearing capacity factors related to cohesion, surcharge, and unit weight of the soil
- $q$ = Surcharge on the soil
- $γ$ = Unit weight of the soil
- $B$ = Width of the footing

In this case, we are considering a bored pile, which can be approximated as a cylindrical footing. Therefore, the width of the footing ($B$) is equal to the diameter of the bored pile (400 mm).

Since the top layer of clay has a thickness of 5 m and the bottom layer is of considerable depth, we can assume that the entire depth of the bored pile is in the bottom layer.

**Step 2: Calculate the bearing capacity factors**

The bearing capacity factors ($N_c, N_q, N_γ$) can be determined based on the soil type and the angle of internal friction of the soil.

For cohesive soils (clay), the bearing capacity factors can be approximated as:
- $N_c = 5.7 + 0.44 \cdot \phi'$ (for φ' ≤ 30°)
- $N_q = 1 + 0.2 \cdot \phi'$ (for φ' ≤ 30°)
- $N_γ = 0$

Where:
- $\phi'$ = Effective angle of internal friction of the soil

In this case, we are not given the effective angle of internal friction of the clay, so we cannot calculate the exact bearing capacity factors. However, we can assume conservative values for the bearing capacity factors based on typical values for clay soils.

Assuming $\phi' = 0°$ for clay soils, we can calculate the approximate bearing capacity factors as:
- $N_c = 5.7 + 0.44 \cdot 0° = 5.7$
- $N_q = 1 + 0.2 \cdot 0° = 1$
- $N_γ = 0$

**Step 3: Calculate the ultimate bearing capacity**

Substituting the values into the ultimate bearing capacity formula, we get:

$Q_u = cN_c + qN_q + 0.5γBN_γ$

Since the bottom layer of soil has a higher shear strength, we will use the shear strength of the bottom layer (100 kN/m2) as the cohesion (c) value. The surcharge on the soil (q) can be assumed