## Time and work

##### This topic has expert replies
Master | Next Rank: 500 Posts
Posts: 379
Joined: 30 Sep 2008
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,$419 (Adding five answer choices to make it look like a GMAT question ..LOL) Legendary Member Posts: 1556 Joined: 14 Aug 2012 Thanked: 448 times Followed by:34 members GMAT Score:650 by theCodeToGMAT » Tue Nov 05, 2013 9:56 am A's rate = 1/6 B's rate = 1/12 Workdone in 2 days = 2 (1/6 + 1/12) = 2 (3/12) = 1/2 Left work = 1 - 1/2 = 1/2 Work done by B alone in 3 days = 3/12 = 1/4 Total workdone left = 1/2 - 1/4 = 1/4 A's work = 2(1/6) + 1/4 = 4+3/12 B's work = 2/12 + 3/12 = 5/12 Ratio A:B = 7:5 So, A's share 7/12 * 1008 = 7*84 = 588$

R A H U L

GMAT Instructor
Posts: 15537
Joined: 25 May 2010
Location: New York, NY
Thanked: 13060 times
Followed by:1901 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.