Among the compounds A and B with molecular formula C$$_9$$H$$_{18}$$O$$_3$$, A is having higher boiling point than B. The possible structures of A and B are:

Boiling point of isomeric organic compounds is governed mainly by two factors:
  • the strength of the intermolecular forces they can develop, the strongest of which for neutral molecules is hydrogen bonding.
  • the surface area of contact between molecules (branching lowers surface area and hence lowers boiling point).

Considering the molecular formula $$C_9H_{18}O_3$$, any isomer will contain exactly three oxygen atoms. If those three oxygens appear as three hydroxyl groups (-OH), the molecule can act simultaneously as three hydrogen-bond donors and three hydrogen-bond acceptors, giving rise to an extensive intermolecular hydrogen-bond network. Such a compound therefore boils at a comparatively high temperature.

If, on the other hand, the three oxygens appear as ether oxygens (-O-) or are involved in intramolecular hydrogen bonding, the molecule can serve only as hydrogen-bond acceptor (or not at all), so the intermolecular attraction becomes much weaker and the boiling point drops sharply. Additional branching of the carbon skeleton lowers the boiling point still further.

In Option A (the key), compound A is an open-chain triol: it contains three free hydroxyl groups and is almost unbranched. It develops strong inter-molecular hydrogen bonding and possesses a large surface area, so it has the higher boiling point.

Compound B in the same option contains the same three oxygen atoms, but two of them are present as ether linkages while only one appears as a hydroxyl group. Because most of its oxygens cannot donate hydrogen, and because its skeleton is significantly more branched, the intermolecular attractions in B are far weaker. Consequently B boils at a lower temperature than A.

None of the other options satisfy both of the following simultaneously:
  • one structure capable of extensive intermolecular hydrogen bonding,
  • an isomeric partner in which such bonding is largely absent or restricted.
Hence they cannot account for the stated observation “A has a higher boiling point than B”.

Therefore the correct choice is:
Option A which is: (A = the triol, B = the less-hydrogen-bonded ether/isomer).