Two workers $A$ and $B$ working together completed a job in $5$ days. If $A$ worked twice as efficiently as he actually did and $B$ worked $\frac{1}{3}$ as efficiently as he actually did,the work would have completed in $3$ days. Find the time for $A$ to complete the job alone (in days).
- A$6 \frac{1}{2}$
- B$6 \frac{1}{4}$
- C$6 \frac{3}{4}$
- D$12 \frac{1}{2}$
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