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    Question

    A child can do 1/3 rd. of work in same time as his

    father can do the whole work and efficiency of child’s mother is equal to half the sum of father and child efficiency. If they complete 60% of work in 28 days, when they work alternatively, starting with father and child together on first day followed by father and mother together on second day. Find in how many days mother can complete 80% of work alone? 
    A 48 days Correct Answer Incorrect Answer
    B 84 days Correct Answer Incorrect Answer
    C 62 days Correct Answer Incorrect Answer
    D 72 days Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    Let efficiency of child and father be x unit/day and 3x unit/day    Efficiency of mother = (x + 3x)/2 = 2x unit/day   ATQ,  They start work alternatively— First day efficiency = (3x + x) = 4x Second day efficiency= (3x + 2x) = 5x     Total work = {[4x × 14 + 5x × 14]/60} × 100 = {126x/60} ×100 = 210x   Mother complete 80% of work in = [210x × (80/100)]/2x = (168x/2x) = 84 days

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