Discussion
A, B, and C can do a job in 6, 12 and 15 days respectively. After 1/8 of the work is completed, C leaves the job. Rest of the work is done by A and B together. Time taken to complete the rest of the work is:
Answer: A
Work in rates: someone who finishes a job in \( n \) days does \( \tfrac{1}{n} \) of it a day, and rates add.
Once \( \tfrac{1}{8} \) is done, \( \tfrac{7}{8} \) remains for A and B:
\[ \frac{1}{6} + \frac{1}{12} = \frac{2 + 1}{12} = \frac{1}{4} \]
\[ t = \frac{7}{8} \div \frac{1}{4} = \frac{7}{8} \times 4 = 3.5 = 3\tfrac{1}{2} \text{ days} \]
C's rate never enters the calculation, since C leaves before the stretch being timed.
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