Work problem

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hey_thr67: Master | Next Rank: 500 Posts; Posts: 299; Joined: Tue Feb 15, 2011 10:27 am; Thanked: 9 times; Followed by:2 members

Work problem

by hey_thr67 » Sun Jun 03, 2012 12:21 am

2 men and 7 boys can do a work in 14 days. 3 men and 8 boys can do the same work in 11 days. Then 8 men and 6 boys can do 3 times the work in how many days ?

A: 12
B: 21
C: 27
D: 15
E: 18

How can I approximate the answer fast ?

Quote

Source: Beat The GMAT — Problem Solving | Sun Jun 03, 2012 12:21 am

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 Jun 03, 2012 12:54 am

hey_thr67 wrote:2 men and 7 boys can do a work in 14 days. 3 men and 8 boys can do the same work in 11 days. Then 8 men and 6 boys can do 3 times the work in how many days ?

2 men and 7 boys does 1/14 of the job in one day.
3 men and 8 boys does 1/11 of the job in one day.

Hence, in one day,

(2m + 7b) = 1/14
(3m + 8b) = 1/11

So, (2m + 7b)/(3m + 8b) = 11/14
--> (28m + 98b) = (33m + 88b)
--> 10b = 5m
--> m = 2b

Hence, in one day one man works twice of a boy.

Now, (2m + 7b) = (4b + 7b) = 11b
And, (8m + 6b) = (16b + 6b) = 22b

As, 2men and 7 boys, i.e. 11 boys completes the work in 14 days, 8 men and 6 boys, i.e. 22 boys will complete the work in 14/2 = 7 days.

Hence, 8 men and 6 boys can do 3 times the work in 3*7 = 21 days.

The correct answer is B.

Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

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