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    Question

    Atul, Qureshi, and Chintu can individually complete a

    certain task in 27 days, 30 days, and 36 days, respectively. They all begin working on the task together, but Chintu stops after 4 days. Additionally, Qureshi leaves 5 days before the task is finished. How many days does it take to complete the entire task?
    A 12 days Correct Answer Incorrect Answer
    B 20 days Correct Answer Incorrect Answer
    C 15 days Correct Answer Incorrect Answer
    D 32 days Correct Answer Incorrect Answer

    Solution

    ATQ,

    Let the total task = 540 units (LCM of 27, 30 and 36) Amount of task done by Atul alone in one day = 540/27 = 20 units Amount of task done by Qureshi alone in one day = 540/30 = 18 units Amount of task done by Chintu alone in one day = 540/36 = 15 units Amount of task done by Atul, Qureshi and Chintu together in 4 days = 4 × (20 + 18 + 15) = 212 units Amount of task done by Atul alone in 5 days = 5 × 20 = 100 units Remaining work = 540 – 212 – 100 = 228 units Time taken by Atul and Qureshi together to complete 228 units work = 228/(20 + 18) = 228/38 = 6 days So the total time taken to complete the task= 6 + 4 + 5 = 15 days 

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