Question: It is 8:00 p.m. When can Hemant get the next bus for Ramnagar from…

In a Data Sufficiency question, a statement is sufficient only if it lets you compute one single, definite value for what is asked. You must always test each statement in isolation first, and only combine them if neither alone gets you there.

1. Statement I only gives the recurring interval - buses run every 30 minutes, with service continuing up to 10 p.m. This only bounds how late the service runs; it does not fix the actual clock times at which any bus departs, so alone it cannot anchor an exact next-departure time relative to 8:00 p.m.

2. Statement II only gives a reference point - a bus left fifteen minutes before 8:00 p.m., i.e., at 7:45 p.m. It gives no interval, so alone it cannot say how soon the next one follows.

3. Combining the two: from Statement II, the last bus left at 7:45 p.m.; from Statement I, the interval is 30 minutes; so the next bus departs at 7:45 p.m. + 30 minutes = 8:15 p.m. - one single definite time.

Since dropping either statement removes either the reference time or the interval, neither statement alone can fix the schedule - confirming both statements together are required, and are sufficient, to answer the question.