Mohan can do a piece of work in 10 days and Sohan can do it in 12 days. They do the work in alternate days. If Sohan starts the work in the first day, in how many days will the work be completed?
My Attempt:
In $10$ days, Mohan can do $1$ work.
In $1$ day, Mohan can do $\frac {1}{10}$ work.
In $12$ days, Sohan can do $1$ work.
In $1$ day, Sohan can do $\frac {1}{12}$ work.
In $1$ day, Mohan and Sohan can do $\frac {1}{10} +\frac {1}{12}$ work.
In $1$ day, Mohan and Sohan can do $\frac {11}{60}$ work.
To do $1$ work, Mohan and Sohan take $\frac {60}{11}$ days.
If they work in alternate days,
To do $1$ work, Mohan and Sohan take $\frac {120}{11}$ work.
But the actual answer given is $11$ days. How do I get that? Please help.
You missed the statement that they work alternate days. It takes two days to do $\frac {11}{60}$ of the work,so after $10$ days they have done $\frac {55}{60}$ o the work. Sohan can then complete it during the $11$th day.