6 workers should finish a job in 8 days. After 3 days came 4

Question

6 workers should finish a job in 8 days. After 3 days came 4 workers join them. How many days do they need to finish the same job?

A. 3 
B. 4 
C. 5 
D. 6 
E. 7

I do not have the OA. sorry for the inconvenience....

Bunuel · Accepted Answer

There are 6*8=48 units of work to be done (1 unit done by 1 worker in 1 day).

After 3 days 3*6=18 units are done and 30 units left to be done.

Now, 6+4=10 workers can do 30 units of the work in 30/10=3 days.

Answer: A.

Hope it's clear.

rohanGmat · Answer

Let Rate of one worker be R
=> (6*R)*8 = 1 (Rate * Time = work)
=> R = 1/48
=> Work remaining after 3 days 
1 - (3*6)/48 = 30/48

After 4 ppl joined in 
((6+4)*Time)/48 = 30/48
Time = 3 days to finish the task 
IMO A

jeffcarl · Answer

I agree with the math of both of the previous answers, just a question regarding wording: the question asks for "How many days do they need to finish the same job?," which in my mind is the 3 days that the 6 workers use, PLUS the 3 days that the 10 workers use, making the answer D. Thoughts?

Amodita · Answer

Completely agree with Jeffcarl... I got 3+3 =6 days...

Posted from my mobile device

dave785 · Answer

I originally picked D as well, for the same reason.. but after reviewing it again.

"how many days do they need to  finish  the same project?"

well the project as a whole takes 6 days, but only 3 days left to finish it.

Bunuel · Answer

Yes, that's correct. The question asks: "how many days do they need to  finish  the same job?"

noTh1ng · Answer

Can someone pls review my approach?

6 workers need 8 days for a job. This implies that one worker's rate is 8 / 6 = 4 / 3.

Rate of one worker = 4 / 3 times the new number of workers (6+4 = 10):
4/3 * 10 = 40/3 is the rate for all workers.

Take the reciprocal: 3 / 40 implies that they need 3 weeks for the work of 40.

Is this correct or did i just got lucky? Thanks!

GMATinsight · Answer

You have made a sever mistake of this topic in the calculation you have shown 
 6 workers need 8 days for a job. This implies that one worker's rate is 8 / 6 = 4 / 3.

The highlighted part is a flaw in your process. The correct Understanding of the highlighted part is as mentioned below

6 workers need 8 days for a job. This implies that one worker's rate is 8 * 6 = 48 days to finish the same job

The reason for this interpretation is  Manpower is Inversely Proportional to the Time .

CONCEPT:  i.e. more manpower causes less time to finish the job and Less manpower requires more time to finish the job

Work can be finished in 8 days
Remaining Days = 8-3 = 5 days

Now, 6 workers are joined by 4 more workers i.e. the Manpower Increases from 6 to 10 i.e. 5/3 of previous workforce

therefore New time taken should be reciprocal (Inversely Proportional) i.e. 3/5 of previous time i.e. New time = (5)*(3/5) = 3 days

So they Require 3 more days to finish the work.

Rumsus · Answer

This question is not correctly framed. It has been asked "how many days do they need to finish the work" which means total 3+3 = 6 days.
However OA is given as 3 days which actually answers the question "how many MORE days do they require to finish the work".

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6 workers should finish a job in 8 days. After 3 days came 4

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