As shown in the figure, a system undergoes the process abc ,...

According to the first law of thermodynamics:
$\Delta Q = \Delta U + \Delta W$

For the process $abc$, the heat absorbed is $Q_{abc} = 80 \text{ J}$ and the work done is $W_{abc} = 30 \text{ J}$.
The change in internal energy is:
$\Delta U = Q_{abc} - W_{abc}$
$\Delta U = 80 - 30 = 50 \text{ J}$

Since internal energy is a state function, the change in internal energy $\Delta U$ depends only on the initial and final states. Thus, $\Delta U$ is the same for both paths $abc$ and $adc$.

For the process $adc$, the work done is $W_{adc} = 10 \text{ J}$.
The heat absorbed during this process is:
$Q_{adc} = \Delta U + W_{adc}$
$Q_{adc} = 50 + 10 = 60 \text{ J}$