Problem Solving

vaibhav101 wrote:A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work alone in 44 days. In how many days shall B finish the whole work alone?
A 30 days
B 40 days
C 60 days
D 70 days
E 100 days

We can PLUG IN THE ANSWERS, which represent B's time to produce the entire job alone.
Since B takes 44 days to produce part of the job, B's time to produce the entire job must be more than 44 days.
Eliminate A and B.
When the correct answer is plugged in, the time for B to complete the job after A works for 16 days = 44 days.

D: 70 days
Let the job = 210 units.
Since B takes 70 days to produce the 210-unit job, B's rate = w/t = 210/70 = 3 units per day.
Since A and B together take 30 days to produce the 210-unit job, the combined rate for A+B together = w/t = 210/30 = 7 units per day.
A's rate alone = (rate for A+B together) - (B's rate alone) = 7 - 3 = 4 units per day.
Work produced by A in 16 days = rt = 4*16 = 64 units.
Remaining work = 210 - 64 = 146 units.
Since B's rate = 3 units per day, the time for B to produce the remaining 146 units = w/r = 146/3 = 48.66 days.
Here, B takes TOO LONG to finish the job.
Implication:
To finish the job in only 44 days, B must work FASTER, implying that B must take LESS TIME to produce the entire job.

The correct answer is C.

B: 60 days
Let the job = 60 units.
Since B takes 60 days to produce the 60-unit job, B's rate = w/t = 60/60 = 1 unit per day.
Since A and B together take 30 days to produce the 60-unit job, the combined rate for A+B together = w/t = 60/30 = 2 units per day.
A's rate alone = (rate for A+B together) - (B's rate alone) = 2 - 1 = 1 unit per day.
Work produced by A in 16 days = rt = 1*16 = 16 units.
Remaining work = 60 - 16 = 44 units.
Since B's rate = 1 unit per day, the time for B to produce the remaining 44 units = w/r = 44/1 = 44 days.
Success!