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alltimeacheiver: Master | Next Rank: 500 Posts; Posts: 183; Joined: Wed Feb 09, 2011 3:08 am; Location: Delhi; Thanked: 1 times; Followed by:5 members

Work and Rate

by alltimeacheiver » Sun Mar 13, 2011 10:06 pm

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

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Source: Beat The GMAT — Problem Solving | Sun Mar 13, 2011 10:06 pm

GMAT/MBA Expert

Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Sun Mar 13, 2011 11:04 pm

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.

Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
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