Step 1: Separate the two big categories of lung disease.
Obstructive disease narrows the airway, so air comes out slowly and $FEV_1/VC$ drops. Restrictive disease stiffens or shrinks the lung itself, so both $TLC$ and $VC$ fall but the ratio of $FEV_1$ to $VC$ stays normal, since whatever air is inside still leaves at a normal rate.
Step 2: Read the numbers given.
The question gives a fall in $TLC$ and $VC$ together with a normal $FEV_1/VC$ ratio. That is the signature of a restrictive problem.
Step 3: Add in the exam finding.
Bilateral basal crepitations point to fibrous scarring at the lung bases, which is exactly what happens in idiopathic pulmonary fibrosis. The scar tissue makes the lung stiff and small, matching the restrictive numbers.
Step 4: Eliminate the obstructive options.
Chronic bronchitis, cystic fibrosis, and allergic bronchopulmonary aspergillosis all narrow the airways and would drop the $FEV_1/VC$ ratio, which does not match the normal ratio given here.
Step 5: Conclude.
The diagnosis that fits a restrictive pattern with basal crepitations is idiopathic pulmonary fibrosis.
\[ \boxed{\text{Idiopathic pulmonary fibrosis}} \]