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    Question

    Three individuals, 'A', 'B', and

    'C', are employed to complete a task. How many days will it take for 'A', 'B', and 'C' to finish the work together? Statement I:  'C' requires the same amount of time to complete the work as 'A' would if 'C' operates at 125% efficiency. 'B' can complete the task in 12 days, and 'A' and 'B' together finish it in 48/7 days. Statement II:  'A' can finish the task in 20 days when working at 80% efficiency, while 'B' requires 8 days less than 'C' to complete the task. The question consists of two statements numbered "l and II "given below it. You have to decide whether the data provided in the statements are sufficient to answer the question.
    A The data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question. Correct Answer Incorrect Answer
    B The data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question. Correct Answer Incorrect Answer
    C The data either in statement I alone or in statement II alone are sufficient to answer the question. Correct Answer Incorrect Answer
    D The data given in both statements I and II together are not sufficient to answer the question. Correct Answer Incorrect Answer
    E The data in both statements I and II together are necessary to answer the question. Correct Answer Incorrect Answer

    Solution

    ATQ, Statement I: Let, time taken by 'C' to do the work with 100% efficiency = y days So, time taken by 'C' to do the work with 125% efficiency = 4y/5 days Therefore, time taken by 'A'  to do the work = 4y/5 days Work done by 'A' and 'B' in one day = 5/4y + 1/12 = (15 + y)/12y So, (15 + y)/12y = 7/48 60 + 4y = 7y 3y = 60, y = 20 Therefore, 'C' will take 20 days to do the work with 100% efficiency. Work done by all three in one day = 1/20 + 7/48 = (12 + 35)/240 = 47/240 Required number of days = 240/47 days Statement I alone is sufficient to answer the question Statement II: Number of days taken by 'A' to do the work with 100% efficiency = 20 × 4/5= 16 days Let, time taken by 'B' to do the work = x days Then, time taken by 'C' to do the work = (x + 8) days Statement II alone is not sufficient to answer the question.

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