Question

5. A, B and C can do a work sepa-
rately in 16, 32 and 48 days re-
spectively. They started the work
together but B left off 8 days and
C six days before the completion
of the work. In what time is the
work finished?
(1) 10 days (2) 9 days
(3) 12 days (4) 14 days​

Answer 1

A alone can do the work in 16 days, so A completes (1/16) part of the work in one day.

B alone can do the work in 32 days, so B completes (1/32) part of the work in one day.

C alone can do the work in 48 days, so A completes (1/48) part of the work in one day.

Given that B left off 8 days and C six days before the completion of the work.

Let the three worked together for $x$ days, after which B left.

Then A and C worked together for 8 - 6 = 2 days.

Then C left, and so A completed the remaining work in 6 days. This is actually happened.

And also the total work is done in $x+2+6=x+8$ days.

Hence the total work done is given by (representing it as unity),

$\longrightarrow\left(\dfrac{1}{16}+\dfrac{1}{32}+\dfrac{1}{48}\right)x+\left(\dfrac{1}{16}+\dfrac{1}{48}\right)2+\dfrac{1}{16}\times6=1$

$\longrightarrow x=4$

Therefore, the total work is done in $4+8=\bf{12}$ days.

Hence (3) is the answer.