A and B working together completed a job in 5 days. If A works twice as efficiently as he actually did and B works $$\frac{1}{3}$$ of actual efficiency, the work would have completed in 3 days. Find the for A to complete the job alone.

One Day's work of A and B together,
$$\frac{1}{{\text{A}}} + \frac{1}{{\text{B}}} = \frac{1}{5}\,........({\text{i}})$$

When A works with twice efficiency,Then,
$$\frac{2}{{\text{A}}} + \frac{1}{{3{\text{B}}}} = \frac{1}{3}\,........({\text{ii}})$$

on solving equations (i) and (ii), we get
$$A = \frac{{25}}{4} = 6\frac{1}{4}$$