SOLUTION: Ram can do a piece of work in 8 days while shyam alone can do in 12 days. Ram starts doing the work and they work at it alternately for a day. In how many days will the work be fin

Each day Ram works he does 1/8 of the piece of work
Each day Shyam works she does 1/12 of the piece of work.

Get common denominator:

1/8 = 3/24
1/12 = 2/24

Day 1:  3/24 of work is done.
Day 2:  3/24 + 2/24 = 5/24 of work is done.
Day 3:  5/24 + 3/24 = 8/24 of work is done
Day 4:  8/24 + 2/24 = 10/24 = 5/12 of work is done 
Day 5:  10/24 + 3/24 = 13/24 of work is done
Day 6:  13/24 + 2/24 = 15/24 = 5/8 of work is done
Day 7:  15/24 + 3/24 = 18/24 = 3/4 of work is done
Day 8:  18/24 + 2/24 = 20/24 = 5/6 of work is done
Day 9:  20/24 + 3/24 = 23/24 of work is done
Day 10: Since there is only 1/24 of the work left to do,
Shyam only works half a day.

Answer: Ram works on days 1,3,5,7,9 or  5 full days 
        Shyam works on days 2,4,6,8, and half a day on 
        day 10, or  days
        
        5 +  =  days. 

Edwin