Choose the correct phrase from the given options to complete the give…

The correct answer is Option (2) → had started

Past perfect with "by the time":

• The sentence has two past actions: we reached the theatre and the movie started. The movie started first.
• Of two past actions, the earlier one takes the past perfect and the later one takes the simple past.
  • Past perfect: had + past participle
  • Common signal: "By the time" + simple past
• Complete sentence: By the time we reached the theatre, the movie had started.

Why the Other Options are Incorrect?

Option 1: will have started — Incorrect.

• The future perfect is for an action complete before a point in the future.
• It goes with a present-tense time clause ("By the time we reach"), not with the past "reached".
  Example: By the time we reach the theatre, the movie will have started.

Option 3: has started — Incorrect.

• The present perfect links the past with now.
• It cannot be paired with a finished past action such as "we reached".
  Example: Hurry up, the movie has started.

Option 4: is starting — Incorrect.

• The present continuous describes something happening now or very soon.
• It does not fit a sentence set in the past.
  Example: Take your seats, the show is starting.

Contrast: the earlier of two past actions takes “had started”. “Has started” links the past with now, and “will have started” looks ahead to a point in the future.