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    Question

    Two workers, 'X' and 'Y', can

    complete a task on their own in 18 days and 30 days, respectively. If they work on alternate days, beginning with 'X', how many days will it take to finish the work?
    A 23 days Correct Answer Incorrect Answer
    B 27 days Correct Answer Incorrect Answer
    C 17 days Correct Answer Incorrect Answer
    D 13 days Correct Answer Incorrect Answer

    Solution

    Let the total work be the LCM of [18, 30] = 90 units. So, the efficiency of 'X' = (90/18) = 5 units/day. Efficiency of 'Y' = (90/30) = 3 units/day. Work done on the first day by 'X' = 5 units. Work done on the second day by 'Y' = 3 units. So, the work done in two days = 5 + 3 = 8 units. Amount of work done in 22 days = 8 × 11 = 88 units. The remaining 2 units will be completed by 'X' on the 23rd day.

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