A can finish a piece of the work in 16 days and B can finish it in 12 days. They worked together for 4 days and then A left. B finished the remaining work. For how many total number of days did B work to finish the work completely?

9

A = 16 days, B = 12 days,

⇒ Here, A worked for 4 days, therefore,

⇒ Work done by A in 4 days = 3 x 4 = 12        (Efficiency x Time = Work)

Now, Remaining work = 48 - 12 = 36

Here, remaining work is done by B in the whole time(including 4 days),

So, time taken by P to do the work = \(\frac{36}{4}\) = 9 days.

Therefore, the whole work is done in 9 days.