Problem Solving

x2suresh wrote:A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed?

A. 18 days
B. 27 days
C. 26.67 days
D. 16 days
E. 12 days
_________________

together they would take :

1/20+1/30 = 1/12 and that's equivalent to 12 days to do the job
this means that A quited after completing the second day...
so: A did 2/20 =1/10 of the job
B did 2/30 =1/15 of the job on the second day
together they did (1/10)+(1/15) = 1/6 of the job
if B takes 30 days to do 1 job; how much time would he take to do 1-(1/6) of the job?
R: 5/6 * 30= 25 days
so the full time = 25 days of B's work plus 2 days of (B+A)'s work = 27 days
the answer is B


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

n-10 (50/600) = 2/3

n-10 = (2/3) * 12=8

n=18

DarkKnight wrote:Can you please post the OA?

sanju09 wrote:

DarkKnight wrote:Can you please post the OA?

B alone working for the last 10 days would finish 1/3 of the total work. This means that the unit (A & B) must have already completed 2/3 of the work at the rate of 1/12 part of work per day, which would have taken them to work for 8 days together. Thus the whole work was completed in 8 + 10 = 18 days; and that's the OA.

naaga wrote:

sanju09 wrote:

DarkKnight wrote:Can you please post the OA?

B alone working for the last 10 days would finish 1/3 of the total work. This means that the unit (A & B) must have already completed 2/3 of the work at the rate of 1/12 part of work per day, which would have taken them to work for 8 days together. Thus the whole work was completed in 8 + 10 = 18 days; and that's the OA.

thanks buddy

sanju09 wrote:A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed?

A. 18 days
B. 27 days
C. 26.67 days
D. 16 days
E. 12 days

GMATGuruNY wrote:

sanju09 wrote:A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed?

A. 18 days
B. 27 days
C. 26.67 days
D. 16 days
E. 12 days

Plug in job = 60 units.
Rate for A alone = w/t = 60/20 = 3 units per day.
Rate for B alone = w/t = 60/30 = 2 units per day.
Combined rate for A+B together = 3+2 = 5 units per day.
Work completed by B alone in 10 days = r*t = 2*10 = 20 units.
Work to be completed by A+B = 60-20 = 40 units.
Time for A+B to complete 40 units = w/r = 40/5 = 8 days.
Total time = 10+8 = 18 days.

The correct answer is A.

Anurag@Gurome wrote:

diebeatsthegmat wrote:i thought A and B work together in a couple of days then A quit and B continue working on the left job?

According to the question, A and B start working on the project together and A quits 10 days before the project is completed. Now mathematically the event is same as B worked alone for 10 days and then A joined with him! In both of the cases total number of days required will be same.