Question

$A$ can lay railway track between two given stations in $16$ days and $B$ can do the same job in $12$ days. With help of $C$, they did the job in $4$ days only. Then, $C$ alone can do the job in:

• A. $9\frac{1}{5}$ days
• B. $9\frac{2}{5}$ days
• C. $9\frac{3}{5}$ days
• D. $10$

Answer 1

The correct option is C $9\frac{3}{5}$ days

$(A+B+C)$'s $1$ day's work $=\frac{1}{4}$
$A$'s $1$ day's work $=\frac{1}{16}$;
$B$'s $1$ day's work $=\frac{1}{12}$;
$\therefore$ $C$'s $1$ day's work $=\frac{1}{4}-(\frac{1}{16}+\frac{1}{12})=(\frac{1}{4}-\frac{7}{48})=\frac{5}{48}$
So, $C$ alone can do the work in $\frac{48}{5}=9\frac{3}{5}$ days