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A and B can complete a piece of work together in 5 days. If A works at bwice his speed and B at half of his speed, the work can be finished in 4 days. How

many days would it take for A alone to complete the work?



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A can do work in X number of days
B can do work in Y number of days

Per day they can do:  1/X + 1/Y  together.
in 5 days :  5/X + 5/Y.  = total Work amount

2 * 1/X + 1/2 * 1/B = work per day after they change their speeds
     4 * (2/X + 1/2*B)  = total work = 5/X + 5/Y
     1/X * 3 = 1/Y * 3      => X = Y

   Hence the total work =  1/X * 5 + 1/X * 5 = 10 * 1/X
   number of days for A to complete alone:  (10/X)  /  (1/X) =  10 days

1 5 1
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