A can do a certain work in 16 days. B is 50% more efficient then A. How many days will B and A together take to do the same job?

6\(\frac{2}{13}\) days

Ratio of efficiency of A and B = A   :   B

                                              5   :   8     

Ratio of time taken ∝ \(\frac{1}{efficiency}\)  

Ratio of taken taken    A  :  B 

                                 8  :  5   ⇒  (5 x 2 = 10)    

                                 ↓              

                              16(given)     

Total work = L.C.M  of 10 & 16 = 80

Time taken A and B together = \(\frac{Total\; work}{Efficiency}\)

                                          = \(\frac{80}{13}\) = 6\(\frac{2}{13}\) days