A and B together can do a piece of work in 12 days which B and C together can do in 16 days. After A has been working at it for 5 days and B for 7 days, C finishes it in 13 days. In how many days B alone could finish the work?

48

Let total work = 48

(A + B) : (B + C)

    12     :    16              Days 

     4      :     3               Efficiency 

Here,

Say, A works for 5 and B works for 5 days with A and

B works for 2 more days with C.

So,

⇒ Work done by (A + B) in 5 days = 5 x 4 = 20

⇒ Work done by (B + C) in 2 days = 2 x 3 = 6

Remaining work done by C in 11 days = 48 - 26 = 22

⇒ Efficiency of C = 2, similarly B = 1, A = 3

B alone finishes the work in \(\frac{48}{1}\) = 48 days