Question

$A$ can do a job in $16$ days and $B$ can do the same job in $12$ days With the help of $C$, they can finish the job in $6$ days only. Then, $C$ alone can finish it in

• A. $34$ days
• B. $22$ days
• C. $36$ days
• D. $48$ days

Answer 1

The correct option is D $48$ days

We know that,
Number of days $A$ requires to do piece of work $=16$ days

Number of days $B$ requires to do piece of work $=12$ days

Let us consider number of days $C$ requires to do piece of work $=x$ days

Number of days $A,B$ and $C$ together requires to do the piece of work $=6$ days

$\therefore$ We can calculate, work done by $A$ in $1$ day $=1/16$
Work done by $B$ in $1$ day $=1/12$
Work done by $C$ in $1$ day $=1/x$

Work done by $A,B$ and $C$ together in a $1$ day $=1/6$

Now, work done by $A,B$ and $C$ together in $1$ day is also equal to the sum of work done by each of them in $1$ day $=1/16+1/12+1/x=7/48+1/x$

Therefore,

$7/48+1/x=1/6$
$(7x+48)/48x=1/6$
$42x+288=48x$
$6x=288$

$x=288/6=48$

$\therefore C$ can do the work in $48$ days.