Step 1: Understand the question.
Under Section 167 of the CrPC, 1973, an accused gets default bail (also called statutory bail) if the investigation is not completed within a certain time. We must find that time period.
Step 2: What is default bail?
Default bail is a safeguard. It means the police cannot keep an accused in custody forever without filing a charge sheet. If they miss the deadline, the accused earns the right to bail.
Step 3: Recall the two time limits.
The maximum detention period depends on how serious the offence is. For very serious offences (punishable with death, life imprisonment, or imprisonment of not less than ten years), the limit is 90 days. For all other offences, the limit is 60 days.
Step 4: What happens after the limit?
If the investigating agency fails to file the charge sheet within these periods, the accused becomes entitled to be released on bail, provided he is ready to furnish bail.
Step 5: Match with the options.
Option D says after 60 days or 90 days, depending on the maximum punishment for the offence. That captures the rule exactly.
Step 6: Eliminate the wrong options.
Option A (after 15-day police custody) is wrong, as that is about custody type, not default bail. Option B (120 days for offences against the State) is not the correct figure here. Option C (fixed 30 days for all offences) is wrong because the periods are 60 or 90 days, not 30.
Step 7: Final answer.
\[ \boxed{\text{After 60 days or 90 days, contingent upon the maximum punishment prescribed for the offence.}} \]