A can do a piece of work in 36 days and B in 54 days. How many days will both take together to complete the work? 

18

Total work = L.C.M. of time taken by individual workers

Efficiency = \(\frac{Total\; work}{No.\; of\; days}\)

Therefore,         A  :  B

  No. of days    36  :  54   → L.C.M. = 90

 Efficiency         2   :  3   Total= 5

When they work together, efficiency = 5

Say, total work = 90

Thus, No. of days = \(\frac{90}{5}\) = 18