b will take 30 days.... hope it was helpful..... though kvnmurthy has given better answer

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Let B complete the work in X days.
productivity of B =  1/X  amount per day.
productivity of A = 3 / 2X   amount per day.

Productivity of A and B together is  5 / 2X  amount per day.

   So A and B together can finish the work in  2X / 5 days
     2 X / 5 = 12 days
             X = 30 days.

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