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      Question

      In how many days can ‘Q’ alone complete the

      work? I. P, Q and R together can complete the work in 9`(3)/(13)`   days. II. P and Q together can complete the work in 10 days, Q and R together the work together in 20 days, and P and R together can complete the work in 15 days. Each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer – 
      A If the data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question. Correct Answer Incorrect Answer
      B If the data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question. Correct Answer Incorrect Answer
      C If the data either in statement I alone or in statement II alone is sufficient to answer the question. Correct Answer Incorrect Answer
      D If the data in both statements I and II together are necessary to answer the question. Correct Answer Incorrect Answer
      E If the data even in both statements I and II together are not sufficient to answer the question. Correct Answer Incorrect Answer

      Solution

      From I. (P + Q + R) can do the work in 93/13 days. Hence, from I alone we cannot get the answer. From II.  (P + Q)’s one day work = 1/10 part of the work……… (i) (Q + R)’s one day work = 1/20 part of the work……….. (ii) (P + R)’s one day work = 1/15 part of the work………… (iii) ∴ 2(P + Q + R)’s one day work = 1/10 + 1/20 +1/15 = 13/60 ∴ (P + Q + R)’s one day work =  13/120………….. (iv) By subtracting (iii) by (iv), we get Q’s one day work. ∴ Q’s one day work = 13/120 - 1/15 = 5/120 = 1/24 Hence, from II alone we can get the answer.

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