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Two workers A and B working together completed a job in 5 days. If A had worked twice as efficiently as he actually did, the work would have been completed in 3 days. To complete the job alone, A would require?

Two workers A and B working together completed a job in 5 days. If A had worked twice as efficiently as he actually did, the work would have been completed in 3 days. To complete the job alone, A would require? Correct Answer $${\text{7}}\frac{1}{2}{\text{ days}}$$

L.C.M. of Total Work = 15
One day work of A + B = $$\frac{{15}}{5}$$ = 3 unit/day
One day work of (2A + B) = $$\frac{{15}}{3}$$ = 5 unit/day
Now,
Assume A's efficiency is 2 units, B's is 1 unit.
So, it satisfies the equation of both cases
So, actual efficiency of A is 2 units/day
A alone can complete the work in
$$\eqalign{& = \frac{{{\text{Total work}}}}{{{\text{Efficiency}}}} \cr & = \frac{{15}}{2} \cr & = 7\frac{1}{2}{\text{days}} \cr} $$

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