This is a problem from TOMATO Problem number 2, useful for ISI and CMI entrance exam based on Men and Job.

Problem:

If m men can do a job in d days, then the number of days in which m+r men can do the job is
(A) d+r; (B) ( \frac{d}{m} (m+r)) ; (C) ( \dfrac {d}{m+r} ) ; (D) ( \dfrac {md}{m+r} );

Discussion:

If m men can do a job in d days,
Then m men does ( \frac {1}{d} ) job in 1 day
Then 1 man does ( \frac {1}{md} ) job in 1 day
Then m+r men does ( \frac {m+r}{md} ) job in 1 day
Then m+r men does 1 job ( \frac {md}{m+r} ) days.

Hence answer is ( \dfrac {md}{m+r} ) days (D)

Chatuspathi:

  • What is this topic: Arithmetic
  • What are some of the associated concepts: Unitary Method
  • Where can learn these topics: Cheenta I.S.I. & C.M.I. course, discusses these topics in the ‘Arithmetic’ module.
  • Book Suggestions: Arithmetic by K.C. Nag