A and B can complete a job in 24 days working together. A alone can complete it in 32 days. Both of them worked together for 8 days and then A left. The number of days B will take to complete the remaining job is

Let B will take x days to complete the remaining job.

According to the question,

\( \Large\frac{1}{A} + \frac{1}{B} = \frac{1}{24} \  and  \  \frac{1}{A} = \frac{1}{32}\)

\( \Large\frac{1}{B} = \frac{1}{24} - \frac{1}{32} = \frac{1}{96} \)

= > B = 96 days

According to the question,

\( \Large8 \times \left( \frac{1}{A} + \frac{1}{B}\right) + x \times \frac{1}{B}=1\)

\( \Large 8 \times \frac{1}{24}+ \frac{x}{96}= 1 \)

\( \Large\frac{1}{3} + \frac{x}{96} = 1 \)

\( \Large\frac{x}{96} = 1 - \frac{1}{3} \)

\( \Large x = \frac{2 \times 96}{3} = 64 \)

Hence, B completes the remaining job in 64 days.