Answer : Option A

Explanation :

Note:
(i) Efficiency and time are inversely proportional to each other.
(ii) If 3 efficiencies are given, we have to calculate the time ratio and then reciprocate each efficiency and multiply with the LCM of given efficiencies.
(iii) Efficiency * total days = total work

ATQ,

Efficiency of A: B: C =2: 3: 4
Calculate the LCM of (2, 3, and 4) = 12
Now, reciprocate the efficiencies = ½: 1/3: ¼
Multiply each with 12 and we get time ratio
Time ratio of A: B: C = 12 *[1/2]: 12*[1/3]: 12*[1/4] = 6: 4: 3

The difference between A and B's time ratio = 2, but ATQ, it is 10
i.e., to calculate the days multiply time ratio with 5, then we get 6*5: 4*5: 5*3
The ratio of days= 30: 20: 15
Total work = efficiency * days = 30 * 2= 60, or 20*3= 60, or 15*4= 60
If all three work together
i.e., (A+B+C)'s one day work = 2+3+4 = 9
Or, days required = total work/ (A+B+C)'s one day work
Or, 60/9 = 20/3 = 6[2/3] days
Hence, 6[2/3] days are required to complete the work.