If A quits 10 days before the job is completed, then B alone take 10 days to complete the remaining job.

B's 1 day's work = 1/30

So, B's 10 Days days' work = 10/30 = 1/3

That means, 2/3 of work was completed by A & B Together.

A&B together take = (20x30)/(20+30) Days to complete the full work = 12 Days

To complete 1 unit work A & B take 12 days...

So to complete 2/3 unit of work

A&B would take (2/3)x12 = 8 Days.

Total time to complete the work = (Time take by A&B together + 10 days) = 8+10

18 Days

Option A

(x-10)/20 + x/30 = 1

3x-30+2x=60

5x=90

x=18

Rate * Time = Distance
Let's first start by picking a number that represents 1 complete job. It would be easier if it were the LCD of 20 and 30... Let's say, 60.
So 1 job = 60

A: Rate * 20 = 60
Rate=3
B: Rate * 30 = 60
Rate = 2

They both work together to complete a job except B works the last 10 days by himself. The rate at which they both work together is 3 + 2.
Let t represent time (in days). Therefore the equation is:

5(t-10)+3(10)=60
5t-50+30=60
5t=80
t=18

Answer is A

TOGETHER THEY CAN DO WORK IN 12 DAYS.
A LEFT 10 DAYS BEFORE.ie B WORKED ALONE FOR 10 DAYS.
IN 10 DAYS B COMPLETE 1/3 OF WORK.
SO BEFORE LEAVING 2/3 OF WORK COMPLETED OR FOR 8(2/3 OF 12) DAYS THEY WERE TOGETHER.
SO TOTAL DAYS=10+8=18

A = 1/20 & B = 1/30

Their Combined Rates are: 1/20 + 1/30 = 1/12

The work that is done by both A & B = 1/12*(t-10) = t-10/12

The work that is done by B alone = 1/30*10 = 1/3

The number of day it will take to complete the job is:

(t-10/12) + (1/3) = 1

= 18

OA= A

(B) 27 days

Rate of work by A in one day = 100/20= 5%
Rate of work by B in one day = 100/30= 3.33%
A quit 10 days before the completion means last 10 days B worked alone or he did 3.33 * 10 = 33.33%
Work done by A+B together = (100-33.33)=66.67%
So number of days A and B worked together= 66.67/8.33= 8 days
So total days 8+10 =18 days.

18 days it is.

This was a good question from some dubious source i don't remember ("dubious" because the answers are not in order and the persons are rechristened to be Alphabets already).

A GMAT look to it could have been as under:

Adam can complete a project in 20 days and Brian can complete the same project in 30 days. If they start working on the project together and Adam quits 10 days before the project is completed, in how many days will the project be completed?
(A) 12 days
(B) 16 days
(C) 18 days
(D) 26.67 days
(E) 27 days

What we already know is that their one day work is 1/12 of the total work.

I'd have preferred to plug back the numbers in to the question to check which one works. I'd have preferred to start from (C) for a reason i know.

So, if the project would have been completed in (C) 18 days then Adam must have quitted 8 days after they start, and in those 8 days the part of project done would have been 8/12 or 2/3, and the remaining 1/3 would have been completed by Brian alone in 10 days, which proves that Brian's rate on the project is 1/30 per day.

[spoiler]Hence (C) is correct.[/spoiler]

In 10 days, B will complete 1/3 of work. So before A quits, 2/3 of the work has to be completed. Therefore A and b together will do 1/12 of the work and they will do 2/3 of works in 8 days. Hence My answer is 18.