Multiple choice

Q alone can complete the same job in how many days? (i) The efficiency of R is 25% more than the efficiency of S. (ii) The efficiency of Q is two times more than the efficiency of R. (iii) R and S together can complete the job in 80/3 days. (iv) P and Q together can complete the job in 24 days. Which of the given statements is redundant to find the answer of the question?

  1. Statement (ii)

  2. Statement (iii)

  3. Statement (i)

  4. Statement (iv)

  5. Answer cannot be determined even after using all the statements.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

To find Q's time, we need Q's efficiency. (i) gives R vs S. (iii) gives R+S efficiency. Together (i) and (iii) give R and S efficiencies. (ii) gives Q in terms of R. Thus (i), (ii), and (iii) are sufficient to find Q's efficiency. Statement (iv) relates P and Q, which is not needed to find Q's individual time.

AI explanation

Using statement (i), let the efficiency of S be 4 units per day, making R's efficiency 5 units per day. Statement (ii) specifies that Q's efficiency is two times more than R's, meaning Q's efficiency is 5 + 2(5) = 15 units per day. Statement (iii) establishes the total work as (5 + 4) * (80/3) = 240 units. Therefore, Q alone can complete the job in 240 / 15 = 16 days using only the first three statements, rendering the fourth statement about P and Q completing the job in 24 days entirely redundant. Statement (iv) is redundant to find the answer.

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