The correct answer is D. The project manager asked Vivek how much time he would take to finish this project.
The other options are incorrect because they use the wrong tense. Option A uses the past tense, “would,” which is not appropriate for a question about the future. Option B uses the passive voice, “was asked,” which is also not appropriate for a direct question. Option C uses the future tense, “will be taking,” which is not appropriate for a question about the present.
The correct answer, D, uses the simple present tense, “will take,” which is appropriate for a question about the future. The project manager is asking Vivek to estimate how long it will take him to finish the project.