Tick (✓) the correct answer:
A works twice as fast as B. If both of them can together finish a piece of work in 12 days, then B alone can do it in
(a) 24 days
(b) 27 days
(c) 36 days
(d) 48 days
(c) 36 days
Let A take $x$ days to complete the work. Then B takes $2 x$ days to complete the work.
A's 1 day's work $=\frac{1}{x}$
B's 1 day's work $=\frac{1}{2 x}$
A and B take 12 days to complete the work.
Net work done by $(\mathrm{A}+\mathrm{B})$ in 1 day $=\frac{1}{12}=\frac{1}{x}+\frac{1}{2 \mathrm{x}}=\frac{3}{2 \mathrm{x}}$
$\Rightarrow 2 \mathrm{x}=36$
$\Rightarrow \mathrm{x}=18$
A can complete the work by himself in 18 days.
B will take 36 days, i. e., twice as long as the time taken by A.
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