41. A, B and C can do a piece of work in 16,32 and 48 days
respectively, they start working together but C leaves
after working 4 days and B, 2 days before the
completion of work. Find in how many days the work
was finished?
a) 5 days b) 8 days
c) 10 days d) 12 days
Answers
Step-by-step explanation:
The work is finished in 12 days.
The work is finished in 12 days.
Step-by-step explanation:
Let the work done by A in x days.
Let the work done by B in x-8 days.
Let the work done by C in x-6 days.
Since we have given that
Number of days in which A can finish his work = 16 days
Number of days in which B can finish his work = 32 days
Number of days in which C can finish his work = 48 days
According to question,
\begin{gathered}\frac{x}{16}+\frac{x-8}{32}+\frac{x-6}{48}=1\\\\L.C.M.\ of\ 16,32,48=96\\\\\frac{4x+3(x-8)+2(x-6)}{96}=1\\\\6x+3x-24+2x-12=96\\\\11x-36=96\\\\11x=96+36\\\\11x=132\\\\x=\frac{132}{11}\\\\x=12\end{gathered}
16
x
+
32
x−8
+
48
x−6
=1
L.C.M. of 16,32,48=96
96
4x+3(x−8)+2(x−6)
=1
6x+3x−24+2x−12=96
11x−36=96
11x=96+36
11x=132
x=
11
132
x=12
Hence, the work is finished in 12 days.