M and N can complete a job in 18 days and 20 days, respectively. They worked on it on alternative days starting with M. Find the time taken to comlete it (in day)

Options

A. `18(9)/(10)`
B. 19
C. `18(3)/(5)`
D. `18(3)/(10)`

Answer

A

Explanation

Part of the job completed (by M) on the first day `=(1)/(18)`
Part of the job completed (by N) on the second day `=(1)/(20)`
Part of the job completed on the first 18 days `=(1)/(18)+(1)/(20)=(19)/(180)`
Part of the job completed on the first 18 days . `(18)/(2((19)/(180))=(19)/(20)`
Remaining part `=(1)/(20)`
M work on the 19th day. He can complete the remaining part in `((1)/(20))/((1)/(18))"days"=(9)/(10)` days.
Total time taken `=18(9)/(10)` days