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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)
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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]??
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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.
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