Question

    The question consists of 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. Find the time taken by 'K' and 'L' together to complete the work. 'L' is 28(4/7)% less efficient than 'K'. Statement I: For the same time, 5 times the work done by 'K' is equal to 7 times the work done by 'L'. Statement II: 'K' alone does (4x 2  + 18x + 3 2  - 6x) % of the total work in (2x + 3)  2  days.
    A The data in statement I alone are sufficient to answer the question, while the data in statement II alone is 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 is not sufficient to answer the question. Correct Answer Incorrect Answer
    C The data either in statement I alone or in statement II alone is sufficient to answer the question. Correct Answer Incorrect Answer
    D The data given in both statements I and II together is not sufficient to answer the question. Correct Answer Incorrect Answer
    E The data in both statements I and II together is necessary to answer the question. Correct Answer Incorrect Answer

    Solution

    Let the efficiency of 'K' = 7x units/day

    Then, efficiency of 'L' = 7x X (5/7) = 5x units/day

    Statement I:

    5 X work done by 'K' = 7 X work done by 'L'

    Or, 5 X 7x = 7 X 5x

    Or, 35x = 35x

    So, data in statement I alone is not sufficient to answer the question.

    Statement II:

    Time taken by 'K' to complete the whole work alone:

    = (2x + 3)  2  X {100 ÷ (4x 2  + 18x + 3 2  - 6x) }

    = (2x + 3)  2  X {100 ÷ (4x 2  + 12x + 9) }

    = (2x + 3)  2  X {100 ÷ (2x + 3)  2 } = 100 days

    So, total work = 100 X 7x = 700x units

    So, time taken by K and L together to complete the work:

    = 700x ÷ (5x + 7x)

    = 700x ÷ 12x = 58(1/3) days

    So, data in statement II alone is sufficient to answer the question.

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