In the following question, a sentence is given in direct speech. Select the option that best expresses the same sentence in indirect (reported) speech. My mother said, "I will have cooked the food by then thus I can join you all for the movie."

Introduction / Context:
This question uses a future perfect form combined with a modal of present ability "can". The mother is talking about finishing cooking by a certain future time so that she is free to join the group for a movie. In indirect speech with a past reporting verb, both the future perfect and the modal of ability must be changed appropriately while preserving the cause and effect relationship.

Given Data / Assumptions:

• Reporting verb: "said" in simple past.
• Direct speech: "I will have cooked the food by then thus I can join you all for the movie."
• Pronoun "I" refers to "she" in the reported version.
• Verb phrase "will have cooked" is future perfect.
• Modal "can" expresses present or future ability linked to a future condition.
• Pronoun "you all" refers to "us" in the reported version.

Concept / Approach:
In reported speech after a past reporting verb, "will have" changes to "would have". Modal "can" usually changes to "could". The adverbial phrase "by then" already functions as a relative time marker and does not require change in many exam patterns. The result clause that shows ability must be backshifted from "can" to "could" while still referring to the future in the past. The connector "thus" is often replaced with "so" in the key options, but the meaning remains the same.

Step-by-Step Solution:
Step 1: Start with "My mother said that" for the reporting clause. Step 2: Change "I will have cooked the food by then" to "she would have cooked the food by then". "Will have" becomes "would have", and "I" becomes "she". Step 3: Replace the connector "thus" with "so" which is more common in conversational reported speech. Step 4: Change "I can join you all for the movie" to "she could join us for the movie". "Can" becomes "could", "I" becomes "she", and "you all" becomes "us". Step 5: Combine all parts to get "My mother said that she would have cooked the food by then so she could join us for the movie."

Verification / Alternative check:
The reported sentence still expresses a future perfect action in relation to a point in time referred to as "then", and still links this completed action to the possibility of joining the movie. The backshift from "will have" to "would have" and from "can" to "could" correctly places the whole idea as future in the past. Pronoun changes show clearly who is speaking and who is included in the group watching the movie. The sentence remains grammatically sound and faithful to the original meaning.

Why Other Options Are Wrong:
Option A changes "will have cooked" to "would have cooked" but keeps "can join", which mixes time references. Option B keeps "will have cooked", failing to backshift the future perfect, although it changes "can" to "could". Option D keeps both "will have cooked" and "can join", which does not reflect reported speech after a past reporting verb. Only option C backshifts both verb groups correctly.

Common Pitfalls:
Learners sometimes backshift only the first verb phrase and forget about the modal in the second clause. Others are unsure about whether to change "by then" or leave it, but in many exam patterns "by then" remains unchanged. Focusing on connectors and modals is especially important, as they frequently carry a lot of meaning in complex sentences. Reading through the sentence aloud after conversion often helps catch inconsistent tense patterns.

Final Answer:
The correct reported sentence is My mother said that she would have cooked the food by then so she could join us for the movie.