Multiple choice

Directions: The given question is followed by three statements I, II and III. You have to determine which of the statements is/are necessary/sufficient to answer the question. What is the time taken by P, Q and R together to complete the work if R completes the work in 30 days? I. P is 50% more efficient than R. II. Q is 50% more efficient than P. III. P can complete the work in 20 days.

  1. Only statements I and II are sufficient.

  2. Only statements II and III are sufficient.

  3. Only statement II is sufficient.

  4. Only statement II and either I or III are sufficient.

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

R takes 30 days. P is 50% more efficient than R, so P's time = 30 / 1.5 = 20 days. Q is 50% more efficient than P, so Q's time = 20 / 1.5 = 40/3 days. Statement II provides Q's efficiency relative to P, and either I or III allows finding P's efficiency relative to R or directly. Thus, II and (I or III) are sufficient.

AI explanation

Since the question asks for the combined time of P, Q and R, we need the individual times of all three. We know R takes 30 days. Statement I implies P's efficiency is 1.5 times R's, meaning P takes (30 / 1.5) = 20 days. Statement III independently states P takes 20 days. Thus, either Statement I or III is sufficient to find P's time. Statement II establishes that Q is 1.5 times as efficient as P, meaning Q's time is derived directly from P's time. Therefore, Statement II and either Statement I or III are sufficient to find all three individual times and their subsequent combined time.

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