A composite rod is made of three different materials A, B, and C...

In steady state, the rate of heat flow (heat current) $H$ is constant across all three materials in series.

The heat current is given by $H = \dfrac{KA\Delta T}{L}$.

Since the cross-sectional area $A$ and length $L$ are identical for all three parts, the thermal conductivity $K$ is inversely proportional to the temperature drop $\Delta T$ across that part.

From the given coordinates, the temperature drops are:
$\Delta T_A = 100^{\circ}\text{C} - 70^{\circ}\text{C} = 30^{\circ}\text{C}$
$\Delta T_B = 70^{\circ}\text{C} - 50^{\circ}\text{C} = 20^{\circ}\text{C}$
$\Delta T_C = 50^{\circ}\text{C} - 10^{\circ}\text{C} = 40^{\circ}\text{C}$

Therefore, $K_A \Delta T_A = K_B \Delta T_B = K_C \Delta T_C$
$30 K_A = 20 K_B = 40 K_C$
Dividing by 10, we get $3 K_A = 2 K_B = 4 K_C$.

To find the ratio, let $3 K_A = 2 K_B = 4 K_C = 12x$ (where 12 is the LCM of 3, 2, and 4).
Then $K_A = 4x$, $K_B = 6x$, and $K_C = 3x$.

The ratio $K_A : K_B : K_C$ is $4 : 6 : 3$.

Answer: $4 : 6 : 3$