a) 4 Days
b) 6 Days
c) 8 Days
d) 12 Days
Answer: b
Explanation:
$$\eqalign{
& {\text{Suppose}}\,{\text{A,}}\,{\text{B}}\,{\text{and}}\,{\text{C}}\,{\text{take}} \cr
& x,\,\frac{x}{2},\,\frac{x}{3}\,{\text{days}}\,{\text{respectively}}\,{\text{to}}\,{\text{finish}}\,{\text{the}}\,{\text{work}} \cr
& {\text{Then}},\, {\frac{1}{x} + \frac{2}{x} + \frac{3}{x}} = \frac{1}{2} \cr
& \frac{6}{x} = \frac{1}{2} \cr
& x = 12 \cr
& {\text{So,}}\,{\text{B}}\,{\text{takes}}\, {\frac{{12}}{2}} \cr
& = 6\,{\text{days}}\,{\text{to}}\,{\text{finish}}\,{\text{the}}\,{\text{work}} \cr} $$
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