Correct Answer: $12 \frac{3}{5}$

Solution : Time taken by Raju to complete the work = 20 days
⇒ Part of work done by Raju in a day = $\frac{1}{20}$
Time taken by Sunil to complete the work = 30 days
⇒ Part of work done by Sunil in a day = $\frac{1}{30}$
Time taken by Sunil to complete the work = 40 days
⇒ Part of work done by Sunil in a day = $\frac{1}{40}$
Work done by Raju and Sunil on the first day = $\frac{1}{20}$ + $\frac{1}{30}$ = $\frac{5}{60}$
Work done by Raju and Vishal in the second day = $\frac{1}{20}$ + $\frac{1}{40}$ = $\frac{6}{80}$ = $\frac{3}{40}$
Work done in first 2 days = $\frac{5}{60}$ + $\frac{3}{40}$ = $\frac{10+9}{120}$ = $\frac{19}{120}$
Work done in first (2×6) i.e.12 days = $\frac{19×6}{120}$ = $\frac{114}{120}$
Work left = $1-\frac{114}{120}$ = $\frac{6}{120}$
Work done by Raju and Sunil on 13th day = $\frac{\frac{6}{120}}{\frac{5}{60}}$ = $\frac{3}{5}$
Total time taken = $12 + \frac{3}{5}$ = $12\frac{3}{5}$ days
Hence, the correct answer is 12 $\frac{3}{5}$.