am takes 9 days and Gopal takes D days to complete a job working alone. Ram and Gopal work on the job on alternate days. If they take exactly the same time irrespective of who starts the job,how many positive integer values are possible for D?

• c is the correct choice.
  
  (i) The first trivial solution is at D = 9. In this case it does not matter who starts the job.
  (ii) For the other solutions, the part of the work done in two days which is 1/9 + 1/D must be of the form 1/B where B is a integer.
  In such a case the job will be completed at the end of 2B days. So it would not matter who started the job.
  So, (9+D)/9D = 1/B or 9D/(9+D) = B or [9(9+D) - 81]/(9+D) is an integer.
  Hence 81 must be divisible by 9+D. So D takes the value 18 and 72.
  So Gopal takes any of the 3 values - 9 days, 18 days or 72 days - to complete the
• 10 years agoHelpfull: Yes(1) No(1)