What happens when a saturated solution is heated?

Smoke and fog both are aerosols. In what way are they different?

$A$ solution contains $50 \, g$ of sugar in $350 \, g$ of water. Calculate the concentration of the solution in terms of mass by mass percentage of the solution. (in $\%$)

What happens when a saturated solution is cooled?

You are provided with a solution of substance $'X'$. How will you test whether it is saturated or unsaturated with respect to $'X'$ at a given temperature? What happens when a hot saturated solution is allowed to cool?

$(a)$ Both smoke and fog are aerosols. In what way are they different?
$(b)$ How do sol and gel differ from each other? Give one example for each.