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    Question

    'Asmita,' who is three times as efficient as 'Bittu,' can complete a task on her own in 15 days. 'Asmita' and 'Bittu' began working together, but after 3 days, 'Asmita' departed, and 'Chinky,' who is 25% less efficient than 'Bittu,' took over. 'Bittu' left the job 2 days before its completion, and 'Chinky' completed the remaining work alone. Determine the number of days 'Bittu' and 'Chinky' worked together.

    A 45 days Correct Answer Incorrect Answer
    B 25 days Correct Answer Incorrect Answer
    C 15 days Correct Answer Incorrect Answer
    D 18 days Correct Answer Incorrect Answer
    E none of these Correct Answer Incorrect Answer

    Solution

    ATQ, Since, ‘Asmita’ is thrice as efficient as ‘Bhanu’. Therefore, time taken by ‘Bhanu’ to complete the whole work alone = 3 × 15 = 45 days Let total amount of work = 45 units {LCM of 15 and 45} Efficiency of ‘Asmita’ = 45/15 = 3 units/day Efficiency of ‘Bhanu’ = 45/45 = 1 unit/day Efficiency of ‘Chinky’ = 0.75 units/day Amount of work completed by ‘Asmita’ and ‘Bhanu’ together in the first 3 days = 3 × (1 + 3) = 12 units Amount of work completed by ‘Chinky’ alone in 2 days = 2 × 0.75 = 1.5 units Remaining work = 45 – 12 – 1.5 = 31.5 units Therefore, time taken for which ‘Bhanu’ and ‘Chinky’ worked together  = {31.5/(1 + 0.75)} = 18 days

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