A, B and C can do a piece of work in 15 days. After all the three worked for 2 days, A left. B and C worked for 10 more days and B left. C worked for another 40 days and completed the work. In how many days can A alone complete the work if C can complete it in 75 days?

• 30 days
  
  (1/A)+(1/B)+(1/C)=1/15 ----(i)
  so A, B & C's 2 day work=2/15
  10 days work of B & C= (10/B)+(10/C)
  Remaining work is done by 'C' in 40 days=40/75=8/15
  As (A,B & C's 2 days work)+(B & C's 10 days work)+(C's 40 days work)=complete work
  So (2/15)+[(10/B)+(10/C)]+8/15=1 ----(ii)
  Substituting 1/C=1/75 in (ii) and solving 1/B=1/50
  Substituting values of 1/B & 1/C in (i), we get 1/A=1/30
  So 'A' alone can complete the work in 30 days.
• 9 years agoHelpfull: Yes(1) No(1)
• why should substitute in middle 1/c=1/75 in the problem it is not given before the last statement
  
• 9 years agoHelpfull: Yes(1) No(0)