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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.

Correct Answer: $$6\frac{1}{4}$$
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 $$A = \frac{{25}}{4} = 6\frac{1}{4}$$

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