a and b

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colakumarfanta: Senior | Next Rank: 100 Posts; Posts: 49; Joined: Mon May 03, 2010 2:55 am; Thanked: 1 times

by colakumarfanta » Sun Nov 13, 2011 3:10 am

A along with B can do 1 / 2 of the work in 60 minutes, B is four times faster than A, How long will A take to do rest of the work if it works alone?
A. 50 B. 75 C. 120 D. 150 E. 300

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Source: Beat The GMAT — Problem Solving | Sun Nov 13, 2011 3:10 am

rijul007: Legendary Member; Posts: 588; Joined: Sun Oct 16, 2011 9:42 amFollowed by: 9 members; Location: New Delhi, India; Thanked: 130 times; GMAT Score:720

by rijul007 » Sun Nov 13, 2011 3:24 am

rate of A = a wph (work per hour)
rate of B = b wph

rate of A and B together = (a+b) wph = 1/2 wph

b = 4 a

a + 4a = 1/2
5a = 1/2
a = 1/10
rate of A = 1/10 wph

A would take 10hrs to complete the whole work

A will complete the remaining half of the work in 5 hrs = 5*60 mins = 300 mins

Option E

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sun Nov 13, 2011 3:43 am

colakumarfanta wrote:A along with B can do 1 / 2 of the work in 60 minutes, B is four times faster than A, How long will A take to do rest of the work if it works alone?
A. 50 B. 75 C. 120 D. 150 E. 300

Let the rate for B = 4 units per hour and the rate for A = 1 unit per hour.
Thus, in 60 minutes, A and B produce 1+4 = 5 units.
Since this is 1/2 the work, the remaining amount of work = 5 units.
Time for A to complete the work = w/r = 5/1 = 5 hours.

The correct answer is E.

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