A can do as much work as B and C together can do. A and B can together do a piece of work in 9 hours 36 minutes and C can do it in 48 hours. The time in hours that B needs to do the work alone, is ?

Solution(By Examveda Team)

9 hours 36 minutes
$$\eqalign{ & = 9 + \frac{{36}}{{60}}\,{\text{hours}} \cr & = 9\frac{3}{5} = \frac{{48}}{5}{\text{hours}} \cr} $$
(A + B)’s 1 hour’s work = $$\frac{5}{{48}}$$
C’s 1 hour’s work = $$\frac{1}{{48}}$$
(A + B + C)’s 1 hour’s work = $$\frac{5}{{48}} + \frac{1}{{48}}$$   = $$\frac{1}{8}$$ . . . . . . .(i)
A’s 1 hour’s work = (B + C)’s 1 hour’s work . . . . . . . . (ii)
From equation (i) and (ii),
2 × (A’s 1 hour’s work) = $$\frac{1}{8}$$
A’s 1 hour’s work = $$\frac{1}{{16}}$$
∴ B’s 1 hour’s work
$$\eqalign{ & = \frac{5}{{48}} - \frac{1}{{16}} \cr & = \frac{{5 - 3}}{{48}} \cr & = \frac{1}{{24}} \cr} $$
∴ B alone will finish the work in 24 hours.