work and time (self doubts)

Question

A can do piece of work in 4 hours: B and C  together can do it in 3 hours,while A and C together can do it in 2 hours. how long will B alone take to do it?

Answer 1

Work done by $A$ in $1$ hour =$\frac{1}{4}$

Work done by $B$ and $C$  in $1$ hour=$\frac{1}{3}$

Work done by $A$ and $C$  in $1$ hour=$\frac{1}{2}$


Work done by $A$ ,$B$ and $C$  in $1$ hour=$\frac{1}{4} +\frac{1}{3}=\frac{7}{12}$

Work done by $B$ in $1$ hour $=$ (Work done by $A$ ,$B$ and $C$  in $1$ hour)$-$(Work done by $A$ and $C$  in $1$ hour)

                                                $=$$\frac{7}{12} - \frac{1}{2} = \frac{1}{12}$


$B$ alone will take time to complete his work =12 Hours

Answer 2

Let the work to be done is $12$ units.(Take any number that is divisible by $4,3,2$ like $12,24,36….$ ).

Now since $A$ can do it in $4$ hrs, $A$ completes $3$ units of work per hour.--->$(1)$

$B$ and $C$ can do it $3$ hrs.So together they complete $4$ units of work per hour.--->$(2)$

$C$ and $A$ can do it in $2$ hrs.So together they complete $6$ units of work per hour.--->$(3)$

from statements $(1),(3)$ we can say that A does $3$ units of work per hour.--->$(4)$

from statements $(2),(4)$ we can say that B does 1 unit of work per hour.

So to complete $12$ units of work, $B$ need $12$ hours.

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The $12$ units of work can be anything it can be building $12$ walls, eating $12$ apples,manufacturing $12$ computer etc….