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) $\frac {d}{m+r}$ ; (D) $\frac {md}{m+r}$;
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 $\frac {md}{m+r}$ days (D)
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) $\frac {d}{m+r}$ ; (D) $\frac {md}{m+r}$;
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 $\frac {md}{m+r}$ days (D)
