Time and work

This topic has expert replies
Master | Next Rank: 500 Posts
Posts: 379
Joined: Tue Sep 30, 2008 7:17 am
Location: NY
Thanked: 28 times
Followed by:11 members

Time and work

by abhasjha » Tue Nov 05, 2013 9:20 am
A can finish a piece of work alone in 6 days , while B can finish the same in 12 days .They start working together and A quits after 2 days .Then B works Alone for 3 days and after this A is called back and he finishes the work alone .If they are paid $1008 for the work, find the amount that each one gets assuming that the amount is distributed in the ratio of of work that they do.

(a) $ 673,$ 335
(b) $654,$354
(C) $588,$420
(d)$587,$421
(e) $589,$419 (Adding five answer choices to make it look like a GMAT question ..LOL)

User avatar
Legendary Member
Posts: 1556
Joined: Tue Aug 14, 2012 11:18 pm
Thanked: 448 times
Followed by:34 members
GMAT Score:650

by theCodeToGMAT » Tue Nov 05, 2013 9:56 am
A's rate = 1/6

B's rate = 1/12

Workdone in 2 days = 2 (1/6 + 1/12) = 2 (3/12) = 1/2

Left work = 1 - 1/2 = 1/2

Work done by B alone in 3 days = 3/12 = 1/4

Total workdone left = 1/2 - 1/4 = 1/4

A's work = 2(1/6) + 1/4 = 4+3/12

B's work = 2/12 + 3/12 = 5/12

Ratio A:B = 7:5

So, A's share

7/12 * 1008 = 7*84 = 588$

Answer [spoiler]{C}[/spoiler]??
R A H U L

User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Tue Nov 05, 2013 10:41 am
abhasjha wrote:A can finish a piece of work alone in 6 days , while B can finish the same in 12 days .They start working together and A quits after 2 days .Then B works Alone for 3 days and after this A is called back and he finishes the work alone .If they are paid $1008 for the work, find the amount that each one gets assuming that the amount is distributed in the ratio of of work that they do.

(a) $ 673,$ 335
(b) $654,$354
(C) $588,$420
(d)$587,$421
(e) $589,$419 (Adding five answer choices to make it look like a GMAT question ..LOL)
Let the job = the LCM of 6 and 12 = 12 units.
Since A can complete the job in 6 days, A's rate = w/t = 12/6 = 2 units per day.
Since B can complete the job in 12 days, B's rate = w/t = 12/12 = 1 unit per day.

B works for a total of 5 days (2 days with A, 3 days alone).
Work produced by B in 5 days = r*t = 1*5 = 5 units.
Since B produces 5 of the 12 units, B receives 5/12 of the total pay:
(5/12) * 1008 = 5 * 84 = 420.

The correct answer is C.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3