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In 12 day (A+B) can do a work
hence (A+B) 1 days work =1/12
similarly a's 1 day work =1/20
hence b's alone work= 1/12-1/20=2/60=1/30
 hence b can finish his work in1/1/30= 30 days

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1/A + 1/B  = 1/C    
 A does work in A days, So per day A does 1/A amount
B does in B days, So per day B does 1/B amount
AB together they can do each day  1/A + 1/B  this is equal to 1/12
=> 1/12 = 1/20  + 1/B      solve to get B = 30 days
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