A and B working separately can do a piece of work in 9 and 15 days respectively. If they work for a day alternately, with A beginning, then the work will be complete in :
Q. A and B working separately can do a piece of work in 9 and 15 days respectively. If they work for a day alternately, with A beginning, then the work will be complete in :
Answer: 11 days
Notes: A's 1 day's work $latex = \frac{1}{9}&s=1$ B's 1 day's work $latex = \frac{1}{15}&s=1$ Work done in first 2 days = A's 1 day's work + B's 1 day's work $latex = \frac{1}{9}+\frac{1}{15} = \frac{5+3}{45} = \frac{8}{45}&s=1$ ∴ Work done in first 10 days $latex = \frac{8\times 5}{45} = \frac{8}{9}&s=1$ Remaining work $latex = 1-\frac{8}{9} = \frac{1}{9}&s=1$ Now it is turn of 'A' for the eleventh day. ∴ Time taken by 'A' in doing $latex \frac{1}{9}&s=1$ work $latex = \frac{1}{9}\times 9 = 1\ day&s=1$ $latex \therefore Required\ Time\ = 10+1=11\ days$ Hence option [C] is correct answer.