Question

Find the Number of Days A, B and C Can do the Work Separately
A and B can do a piece of work in 20 days. B and C together can do it in 25 days. A starts the work and work on it for 10 days. Then B takes up the work and work for 15 days. Finally C finishes the work in 17 days. In how many days each can do the work separately?

Answer 1

this  question could be solved by assuming total work, mostly take LCM of days given in question

 Here LCM of 20 and 25 is taken as total work.

 Assume total work =100 units

Then workdone by (A+B) in one day = 100/20 = 5 units , so A+B=5
Similarly, by (B+C) in one day = 100/25 = 4 units .so B+C=4

Now according to question,
A works 10 days , B for 15 days and C for 17 days to complete total work

So, 10A + 15B + 17C = 100 units
5(A+B) + 10(B+C) + 8C = 100 units
 5* 5+ 10* 4+8C =100 units
 
25+40+8C=100
8C=100-65
C=4.3