In the following question, a sentence has been given in Direct speech. Out of the four alternatives suggested, select the one which best expresses the same sentence in Indirect speech: Sheetal said to me, "How have you solved this problem?"

Introduction / Context:
This question focuses on changing a direct question into indirect or reported speech. The original sentence is "Sheetal said to me, How have you solved this problem?" Such transformations are very common in exams and check several skills at once: tense backshifting, change of pronouns, change of time and place references, and conversion of interrogative word order into statement order within the reported clause.

Given Data / Assumptions:

• Direct speech: Sheetal said to me, "How have you solved this problem?"
• Reporting verb: "said to", which will change to "asked" in reported speech because a question is being reported.
• The question begins with "How", a wh-question word.
• The tense inside the quotation is present perfect: "have you solved".
• The phrase "this problem" will normally change to "that problem" in indirect speech.

Concept / Approach:
When converting a present perfect question in direct speech into indirect speech, we typically backshift the tense to past perfect, especially when the reporting verb is in the past tense ("said"). The interrogative word order "have you solved" becomes normal statement order "I had solved" inside the reported clause. The pronoun "you" changes to "I" because the speaker is reporting what was said to them. "This" often changes to "that" to reflect the shift from direct to reported context. Finally, "said to" is replaced by "asked" when the original sentence is a question.

Step-by-Step Solution:
Step 1: Change the reporting verb: "said to me" becomes "asked me" because Sheetal was asking a question. Step 2: Remove quotation marks and add the conjunction "how" directly; wh-words like "how" remain in reported speech. Step 3: Change the subject "you" to "I" since I am the person being addressed. Step 4: Backshift the tense from present perfect "have solved" to past perfect "had solved", consistent with a past reporting verb. Step 5: Change "this problem" to "that problem" to reflect the change in point of view from direct to indirect speech. Step 6: Combine the parts: "Sheetal asked me how I had solved that problem." Step 7: Ensure correct word order, with "I had solved" in statement form, not interrogative form.

Verification / Alternative check:
Check the resulting sentence: "Sheetal asked me how I had solved that problem." It correctly shows that Sheetal wanted to know the method or explanation, uses the appropriate past perfect tense, and replaces the direct second person pronoun with first person. Compare this with general rules of reported speech: present perfect often changes to past perfect when the reporting verb is in the past, and demonstratives like "this" can change to "that". The sentence follows these patterns, so it is a valid indirect form.

Why Other Options Are Wrong:
"Sheetal asked me how I have solved that problem" keeps "have solved" in present perfect, which is inconsistent with the past tense reporting verb and standard exam rules for reported speech. "Sheetal asked me how I had solved this problem" fails to change "this" to "that", which is generally expected in formal reported speech contexts. Any option that keeps the interrogative word order "have I solved" or uses an incorrect conjunction "that how" would not conform to the rule that wh-questions keep the wh-word but switch to statement order inside the clause.

Common Pitfalls:
Students often forget to backshift the tense or to adjust demonstratives like "this" and "that". Another common error is combining "that" and a wh-word, such as writing "asked me that how", which is incorrect. The correct pattern is "asked me how" or "asked me why", etc. Remember to systematically check pronoun changes, tense shifting, and time or place word adjustments whenever you convert from direct to indirect speech.

Final Answer:
The correct indirect form of the given sentence is Sheetal asked me how I had solved that problem.