Time & Work Sum of the day

 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

Ans: 

The rate of A 120$\frac{1}{20}$ job per day;
The rate of B 130$\frac{1}{30}$ job per day.

Say they need t$t$ days to complete the project.

According to the stem we have that B works for all t$t$ days and A works only for t−10$t-10$ days, thus 120∗(t−10)+130∗t=1$\frac{1}{20}\ast (t-10)+\frac{1}{30}\ast t=1$ --> t=18$t=18$days.

or 

Assume to total work to be 60 Units ( LCM of 20 & 30)
A does 3 units per day ( =60/20)
B does 2 units per day ( =60/30)
B works for 10 days alone work done = 2*10 = 20 units
A and B work together for the rest of the time
work left = 40 units
A and b together to 5 units oer day ( 2+3 = 5)
days required to do 40 units = 40/5 = 8

Total = 10+8 = 18