Ajit and Bimal can do a piece of work in 5, and 8 days, respectively, while Chandan can destroy the same work in 12 days. Ajit works on the 1st day, Bimal works on the 2nd day, Chandan works on the 3rd day and so on. They follow the same pattern until the work gets completed. How many days will it take for the work to be completed the first time?

Correct option is B

Given:
Ajit can complete the work in 5 days.
Bimal can complete the work in 8 days.
 Chandan can destroy the same work in 12 days.
Pattern of work: Day 1 Ajit, Day 2 Bimal, Day 3 Chandan, and repeats.
Solution:
Ajit's 1-day work =$$\frac 15$$​
Bimal's 1-day work $$= \frac 18$$​
Chandan's 1-day destruction = $$-\frac 1{12}$$​
Net work in 3-day cycle:
​$$= \frac{1}{5} + \frac{1}{8} - \frac{1}{12} \\\ \\= \frac{24}{120} + \frac{15}{120} - \frac{10}{120}\\\ \\= \frac{29}{120}\\\ \\$$​​
Day-by-day calculation:
​$$\text{Day 1 (Ajit): } \frac{24}{120}\\\ \\\text{Day 2 (Bimal): } \frac{24}{120} + \frac{15}{120} = \frac{39}{120}\\\ \\\text{Day 3 (Chandan): } \frac{39}{120} - \frac{10}{120} = \frac{29}{120}\\\ \\\text{Day 4 (Ajit): } \frac{29}{120} + \frac{24}{120} = \frac{53}{120}\\\ \\\text{Day 5 (Bimal): } \frac{53}{120} + \frac{15}{120} = \frac{68}{120}\\\ \\\text{Day 6 (Chandan): } \frac{68}{120} - \frac{10}{120} = \frac{58}{120}\\\ \\\text{Day 7 (Ajit): } \frac{58}{120} + \frac{24}{120} = \frac{82}{120}\\\ \\\text{Day 8 (Bimal): } \frac{82}{120} + \frac{15}{120} = \frac{97}{120}\\\ \\\text{Day 9 (Chandan): } \frac{97}{120} - \frac{10}{120} = \frac{87}{120}\\\ \\\text{Day 10 (Ajit): } \frac{87}{120} + \frac{24}{120} = \frac{111}{120} = \frac{37}{40}$$​​
​$$\text{Remaining work: } 1 - \frac{37}{40} = \frac{3}{40}\\\ \\\text{Day 11 (Bimal works):}\\\ \\\text{Rate} = \frac{1}{8} \text{ per day}\\\ \\\text{Time needed} = \frac{\frac{3}{40}}{\frac{1}{8}} = \frac{3}{40} \times 8 = \frac{3}{5} \text{ day}$$​​

Total time = 10$$\frac 35$$ days​