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    Question

    Ajay and Vijay together can paint

    a piece of furniture in 11 days. Vijay and Chirag together, as well as Ajay and Chirag together, can paint the same piece of furniture in 13 days and  days, respectively. If each person takes 50% more time to build a piece of furniture than to paint it, what is the time taken by Chirag alone to build the furniture
    A 25 days Correct Answer Incorrect Answer
    B 45.75 days Correct Answer Incorrect Answer
    C 35.75 days Correct Answer Incorrect Answer
    D 15 days Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    ATQ, Let total task = 143 units Combined efficiency of ‘Ajay’ and ‘Vijay’ = 143/11 = 13 units/day Combined efficiency of ‘Vijay’ and ‘Chirag’ = 143/13 = 11 units/day Combined efficiency of ‘Ajay’ and ‘Chirag’ = {143/(143/14)} = 14 units/day Combined efficiency of ‘Ajay’, ‘Vijay’ and ‘Chirag’ = {(13 + 11 + 14)/2} = 19 units/day Therefore, efficiency of ‘Chirag’ = 19 – 13 = 6 units/day Total work in building a wall = 143 × 1.5 = 214.5 units So, time taken by ‘Chirag’ alone to build a wall = 214.5 ÷ 6 = 35.75 days

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