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)

## Time and work

##### This topic has expert replies

- theCodeToGMAT
- Legendary Member
**Posts:**1556**Joined:**14 Aug 2012**Thanked**: 448 times**Followed by:**34 members**GMAT Score:**650

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]??

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

- GMATGuruNY
- GMAT Instructor
**Posts:**15537**Joined:**25 May 2010**Location:**New York, NY**Thanked**: 13060 times**Followed by:**1901 members**GMAT Score:**790

Let the job = the LCM of 6 and 12 = 12 units.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)

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.

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