A can complete a work in 30 days and B can do the same work in half the time taken by A. Working together what part of the work will they complete in 5 days?

\(\frac{1}{2}\)

Time ∝ \(\frac{1}{efficiency}\)

Ratio is reverse for time taken and efficiency

           A  :  B

time     2  :  1

Eff.       1  :  2  total efficiency = 3

Let us say, total work be 30

so, time taken together = \(\frac{Total\; work}{Efficiency}\)

                                   = \(\frac{30}{3}\) = 10 days 

Therefore, in 5 days \(\frac{1}{2}\) of the work will be completed