What will be the sign of work done? Consider the following question:

The enthalpy of vapour is $10\ \mathrm{kcal}/\mathrm{mol}$ higher
than liquid at $350\ \mathrm{K}$ and $2\ \mathrm{atm}$. Under given
conditions, the difference in internal energy of vapour and liquid
will be:
(a) $10700\ \mathrm{cal}$
(b) $-9300\ \mathrm{cal}$
(c) $9300\ \mathrm{cal}$
(d) $-10700\ \mathrm{cal}$

My solution is as follows:
Let the internal energy of the liquid be $U_\mathrm L$ and that of vapor be $U_\mathrm G$. We are required to calculate $U_\mathrm G - U_\mathrm L$. As per the question,
$\because H_\mathrm G = U_\mathrm G + W$, where $H_\mathrm G$ is enthalpy of vapor.
$10000 + U_\mathrm L = U_\mathrm G + W$
Where $W$ is the work done due to the expansion of vapor as the liquid changes state. The magnitude of work done $|W| = \Delta n_\mathrm gRT = 1 \times 2 \times 350 = 700\ \mathrm{cal}$.
Now the real question starts, what is the sign of $W$? As per the IUPAC convention, work of expansion is negative, hence $W = -700\ \mathrm{cal}$. So our answer will come out to be,
$10000 + U_\mathrm L = U_\mathrm G - 700$
$\implies 10000 + 700 = U_\mathrm G - U_\mathrm L$
$\therefore U_\mathrm G - U_\mathrm L = 10700\ \mathrm{cal}$
But the terse solution given to this question is:

As per the solution $W = +700\ \mathrm{cal}$, i.e. they have considered the work of expansion to be positive.
Where are we wrong? Or are we right?
Although the IUPAC convention is for work done by a system to be negative for expansion, many physicists and engineers use the opposite convention. What's important is that you use the same convention throughout your calculation. You wrote that H = U + W, which is true only if work done by the system is regarded as positive. To be consistent with the IUPAC convention that you used later in the calculation, this should be instead H=U - W.

On a side note, since work represents a change in energy, not a state function, this equation should be written in terms of changes: $\Delta H = \Delta U - w$. Also note that this equation is only valid for the condition of constant pressure.