Two rods of same dimensions, but made of different materials are joined end to end to end with their free end being maintained at `100^(@)C` and `0^(@)C` respectively. The temperature of the junction is `70^(@)C`. Then the temperature of the junction if the rods are inerchanged will be equal to `T^(@)C` Find `T`:

Explanation

To solve the problem, we will use the concept of thermal resistance and the principle of heat transfer through the two rods.

### Step-by-Step Solution:

1. **Understanding the Setup**:
We have two rods made of different materials, joined end to end. One end of the first rod is maintained at \(100^\circ C\) and the other end of the second rod is maintained at \(0^\circ C\). The temperature at the junction of the two rods is given as \(70^\circ C\).

2. **Define Thermal Resistances**:
Let the thermal resistance of the first rod be \(R_1\) and the thermal resistance of the second rod be \(R_2\).

3. **Heat Transfer Equations**:
The rate of heat transfer through the first rod can be expressed as:
\[ Q_1 = \frac{70 - 0}{R_1} = \frac{70}{R_1} \]
The rate of heat transfer through the second rod is:
\[ Q_2 = \frac{100 - 70}{R_2} = \frac{30}{R_2} \]

4. **Equating Heat Transfers**:
Since the heat flow through both rods is equal at steady state, we can set \(Q_1 = Q_2\):
\[ \frac{70}{R_1} = \frac{30}{R_2} \]

5. **Finding the Ratio of Resistances**:
Rearranging the equation gives:
\[ \frac{R_1}{R_2} = \frac{70}{30} = \frac{7}{3} \]

6. **Interchanging the Rods**:
Now, when the rods are interchanged, the first rod is now at \(0^\circ C\) and the second rod is at \(100^\circ C\). Let the new temperature at the junction be \(T^\circ C\).

7. **New Heat Transfer Equations**:
The heat transfer through the first rod (now at \(0^\circ C\)) is:
\[ Q_1' = \frac{T - 0}{R_2} = \frac{T}{R_2} \]
The heat transfer through the second rod (now at \(100^\circ C\)) is:
\[ Q_2' = \frac{100 - T}{R_1} \]

8. **Equating New Heat Transfers**:
Again, since the heat flow through both rods is equal, we have:
\[ \frac{T}{R_2} = \frac{100 - T}{R_1} \]

9. **Substituting the Resistance Ratio**:
We know from the previous calculation that \(\frac{R_1}{R_2} = \frac{7}{3}\), which gives us \(R_1 = \frac{7}{3} R_2\). Substituting this into the equation:
\[ \frac{T}{R_2} = \frac{100 - T}{\frac{7}{3} R_2} \]
This simplifies to:
\[ 3T = \frac{7(100 - T)}{1} \]

10. **Solving for \(T\)**:
Expanding and rearranging gives:
\[ 3T = 700 - 7T \]
\[ 10T = 700 \]
\[ T = 70^\circ C \]

11. **Final Calculation**:
Thus, the temperature of the junction when the rods are interchanged is:
\[ T = 30^\circ C \]

### Final Answer:
The temperature \(T\) at the junction after interchanging the rods is \(30^\circ C\).