A and B working separately can complete a piece of work in 10 and 16 days, respectively. If they work for a day alternately, with A beginning the work, in how many day(s) will the work be completed?

Correct option is B

Given:

A can complete the whole work = 10 days 

B can complete the whole work = 16 days 

Solution:

Let the total work = LCM of 10 and 16 = 80 unit

Efficiency of A = $$\frac{80}{10} = 8 unit /day$$

Efficiency of B = $$\frac{80}{16} = 5 unit /day$$

When A and B works alternative days - 

Then the work done by A and B in 12 days = (8+5)$$\times$$6 = 78

Remaining work  = 80 - 78 = 2 unit 

Then A can complete the remaining work = $$\frac{2}{8} = \frac{1}{4}$$ days

Then the total work will be completed = 12 + $$\frac{1}{4}$$   = 12$$\frac{1}{4}$$ days ​