Answer : Option A

Explanation :

ATQ, (A+B) can complete a work in 4 days......................... (i)
Now, the efficiency of A decreases by 30% and B's efficiency is increased by 10%.
i.e., suppose A's and B's efficiency = 1 per day
Then, A = 0.7 and B = 1.1
Or, (0.7 A + 1.1 B) can finish a work in 5 days...................... (ii)

The work will be the same.

Total work = man* days

So, equation 1 = equation 2

(A+B)*4 = (0.7 A + 1.1 B)* 5
Or, 4A + 4B = 3.5A + 5.5B
Or, 0.5A = 1.5B
Or, A: B = 3: 1

That means the efficiency ratio of A and B = 3: 1
Or, total work = Efficiency* days
Or, Total work = (3+1) * 4 = 16

ATQ, the efficiency of A remains same and B's efficiency gets 1[1/2] of the original efficiency.
i.e., A: B = 3: [1 * 1[1/2]]
Or, A: B = 3: 3/2

Now, (A+B)'s one day work = 3+ 3/2 = 9/2

So, days requires = Total work/ efficiency of (A+B)
Or, days = 16/ (9/2), or, 32/9 = 3[5/9]
Hence, 3[5/9] days are required to complete the work.