In the diagram shown, $Q_{iaf}=80\text{cal}$ and $W_{iaf}=50\text{cal}$. If $W=-30\text{cal}$ for the curved path along $fi$, value of $Q$ for path $fi$, will be

The correct option is D $-60\text{cal}$

For the process $iaf$:
First law of thermodynomics says that,
$\Delta Q=\Delta W+\Delta U$
From the data given in the question,
$80=50+\Delta U$
$\Rightarrow \Delta U=30\text{cal}$
Here, the initial state is $i$ and the final state is $f$.
i.e $\Delta U=U_f-U_i=30\text{cal}$
For process $fi$:
Again, applying first law of thermodynamics, we get
$\Delta Q^{\prime }=\Delta U^{\prime }+\Delta W^{\prime }$
Here, $\Delta U^{\prime }=U_i-U_f=-30\text{cal}$
& $\Delta W^{\prime }=-30\text{cal}$ [given]
Therefore, $\Delta Q^{\prime }=-30-30=-60\text{cal}$
Hence, option (d) is the correct answer.