Explanation:

Let total work = 1

For full work let A takes = a days

1 day work of A = 1/a

Similarly, B takes days = b

1 day work of B = 1/b

5 day work of (A+B) is = 5(1/a + 1/b).......................(1)

If A worked twice the original efficiency ,

then 1 day  work of A = 2/a,

If B worked with 1/3 ^rd of the original efficiency

then 1 day work of B = 1/3b

3 day's work of bothe A & B = 3(2/a+1/3b)

Solving we get

4a = b

Putting value of b in =n(1)

5/4a=1/5

a= 6(1/4) days