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    Question

    A can finish a piece of work in 16 days, B in 20 days,

    and C in 24 days. A begins the work, with B joining after 4 days, followed by C joining 2 days later. How many additional days will it take to complete the work?┬а
    A 5 days Correct Answer Incorrect Answer
    B 3.4 days Correct Answer Incorrect Answer
    C 4.4 days Correct Answer Incorrect Answer
    D 6 days Correct Answer Incorrect Answer
    E 7 days Correct Answer Incorrect Answer

    Solution

    Let the total work be 1 unit. AтАЩs efficiency = 1/16, BтАЩs efficiency = 1/20, and CтАЩs efficiency = 1/24. A works alone for the first 4 days: Work done by A in 4 days = 4 ├Ч 1/16 = 1/4. Remaining work = 1 - 1/4 = 3/4. A and B work together for 2 more days: Work done by A and B in 2 days = (1/16 + 1/20) ├Ч 2 = (9/80) ├Ч 2 = 9/40. Remaining work = 3/4 - 9/40 = 30/40 - 9/40 = 21/40. Now, A, B, and C are working together. Their combined efficiency = 1/16 + 1/20 + 1/24 = 37/240. Time taken to complete the remaining work = (21/40) ├╖ (37/240) = 126/37┬а тЙИ 3.4 days. Final Answer: (b) 3.4 days

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