Working together A and B can complete a work in 12 days. They work together for 9 days after which B leaves. If A finishes the remaining work in 5 days, then the number of days that B alone would take to complete the work is:

30

A + B = 12 days,

Let efficiency pf A + B be 2,

Therefore, total work = 2 x 12 = 24 units,   ..(Efficiency × Days = Total work)

⇒ A + B worked for 9 days = 2 x 9 = 18 units,

⇒ Remaining work = 24 - 18 = 6 units,

⇒ B left, so A completed the remaining work in 5 days = \(\frac{6}{A}\) = 5 days, 

⇒ A = \(\frac{6}{5}\)  (Efficiency)

⇒ So B = 2 - \(\frac{6}{5}\) = (\frac{4}{5}\),

Therefore, time taken by B to complete the total work = \(\frac{24}{4/5}\) = 30 days,     ..(\(\frac{Work}{Efficiency}\) = Time)