A) $ 11\frac{5}{7}days $
B) $ 12\frac{5}{7}days $
C) $ 13\frac{5}{7}days $
D) $ 14\frac{5}{7}days $
Correct Answer: C
$ \therefore $ One day work of $ A=\frac{1}{15}\times \frac{5}{8}=\frac{1}{24} $ Time takes by B to complete $ \frac{3}{8}th $ of work = 12 days.
$ \therefore $ One day work of $ B=\frac{3}{8}\times \frac{1}{12}=\frac{1}{32} $ Together A and B one day work $ =\frac{1}{24}+\frac{1}{32} $ $ =\frac{4+3}{96}=\frac{7}{96} $ Hence, they will take $ \frac{96}{7}=13\frac{5}{7}days $ to complete the work together.