Question : A, B, and C can do work separately in 16, 32, and 48 days, respectively. They started the work together, but B left off eight days and C six days before the completion of the work. In what time is the work finished?
Option 1: 10 days
Option 2: 9 days
Option 3: 12 days
Option 4: 14 days
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Correct Answer: 12 days
Solution :
Given: A, B, and C can do work separately in 16, 32, and 48 days.
Let the work be finished in $x$ days.
By applying the formula:
Using, If a man can do the work in $n$ days, then 1 day's work of the man $=\frac{1}{n}$.
According to the question,
$\frac{x}{16}+\frac{x - 8}{32}+\frac{x-6}{48}$ = 1
⇒ $\frac{6x+3x-24+2x-12}{96}$ = 1
⇒ 11$x$ – 36 = 96
$x$ = $\frac{132}{11}$ = 12
Hence, the correct answer is 12 days.
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