Question:

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

Solution:

(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.