alltimeacheiver wrote:Hi Gmat Gins Pls help me with this problem


A, b, C working alone finish consturcting house in 4,6,12 Hrs resp. A starts alone and work 1 hr. He then joined by b and they work together for 1 Hr. Finally c joined then all together to work for rest of the work. They start working 9.00 am in the morning and at what time they finish?

a. 11.30am
b 12.00 pm
c 11.40 am
d 11.10 am
e 11.20 am

1 hr work A, B, and C = 1/4, 1/6, 1/12 respectively.
A finishes 1/4 work in first 1 hr.
1 hr work of A and B = 1/4 + 1/6 = 5/12
Work finished in 2 hrs = 1/4 + 5/12 = 8/12 = 2/3
Remaining work = 1 - 2/3 = 1/3
1 hr work of A, B, and C = 1/4 + 1/6 + 1/12 = 6/12 = 1/2 or A, B, C together can finish 1/2 work in 1 hr or A, B, C together can finish 1 work in 2 hrs.
So, A, B, C can finish 1/3 work in 2/3 hr.
So, total time taken = 2 + 2/3 = 2 hrs 40 minutes
They started working at 9:00 am and finished the work in 2 hrs 40 minutes. So, they finished at 11:40 am

The correct answer is C.