A does half as much work as B in three fourth of the time. If together they take 18 days to complete a work, how much time shall B take to do it alone ?
Three fourth of the work A is equal to half of what B had done.
Work done by A $$=\frac{1}{2} \times \frac{3}{4}$$ Work done by B $$= \frac{2}{3}$$ Work done by B
Work is completed in 18 days when both A and B work together.
$$ 18 \times (A+B)$$ $$=1$$
Replacing A with $$\frac{2}{3}B$$
$$ 18 \times (\frac{2}{3}B+B) =1$$
$$ 18 \times (\frac{5}{3}B) =1$$
$$B=30$$
Hence Option A is the correct answer.
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