According to the question:
A can do a job in = 12 days
B can do a job in = 18 days
A works for 3 days then B joins.
Work done by A in first 3 days = (3 × \(\frac{1}{12}\)) → \(\frac{1}{4}\)
So, work left will be = (\(1 - \frac{1}{4}\)) → \(\frac{3}{4}\)
Work done by A and B together per day = (\(\frac{1}{12}\) + \(\frac{1}{18}\)) = (\(\frac{3}{36}\) + \(\frac{2}{36}\)) → \(\frac{5}{36}\)
Days required for remaining \(\frac{3}{4}\)th work = \(\frac{\frac{3}{4}}{\frac{5}{36}}\) ⇒ \(\frac{3}{4}\) × \(\frac{36}{5}\)
= \(\frac{27}{5}\) → 5.4 days
Thus, total days to finish = 3 days (A) + 5.4 (A + B) → 8.4 days
Hence, "Option 1" is the correct answer.