QUESTION

# A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in

Hint: We will be using a unitary method to solve this question. From the question we can see that B is twice efficient than A and C is thrice efficient than A. If A does 1 unit of work per day, B will do 2 units and similarly C will be doing 3 units.

Let us consider that B takes $x$ days to complete the work alone, so A takes $2x$ days to complete the work.
As it is given in the question that C is thrice as efficient as A, so we get that C takes $\dfrac{2x}{3}$ days to complete the work.
Work done by A, B and C in one day $=\dfrac{1}{2x}+\dfrac{1}{x}+\dfrac{3}{2x}......(1)$
Simplifying equation (1) and equating it to $\dfrac{1}{2}$ because the work is completed in 2 days so this is half the work. So we get,
$\,\Rightarrow \dfrac{6}{2x}=\dfrac{1}{2}......(2)$
$\,\Rightarrow x=6$
Now, A+B+C one-day work $=6$ units.
Since they complete the work in 2 days, so total work will be $2\times 6=12$ units.
B alone will take $\dfrac{12}{2}$ i.e. 6 days.