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 :
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 that B needs to do the work alone, is :
[A]12 hours
[B]18 hours
[C]24 hours
[D]30 hours
24 hours
9 hours 36 minutes =
$latex = 9+\frac{36}{60} = 9\frac{3}{5}\ hours = \frac{48}{5}\ hours&s=1$
(A + B)’s 1 hour’s work $latex = \frac{5}{48}&s=1$
C’s 1 hour’s work $latex = \frac{1}{48}&s=1$
(A + B + C)’s 1 hour’s work $latex = \frac{5}{48} + \frac{1}{48} = \frac{1}{8}&s=1$…………(I)
A’s 1 hour’s work = (B + C)’s 1 hour’s work…………(II)
From equation (I) and (II),
2$latex \times&s=1$(A’s 1 hour’s work) = $latex \frac{1}{8}&s=1$
A’s 1 hour’s work = $latex \frac{1}{16}&s=1$
∴ B’s 1 hour’s work $latex = \frac{5}{48} – \frac{1}{16}&s=1$
$latex = \frac{5-3}{48} = \frac{1}{24}&s=1$
∴ B alone will finish the work in 24 hours.
Hence option [C] is correct answer.