Jake and Ryan worked together on a job for which they were each paid

Question

Jake and Ryan worked together on a job for which they were each paid a dollars in advance. If Jake spent 20% more time working on the job than Ryan did, and Ryan gave Jake b dollars, so that their hourly wages were equal, then, in terms of b, how much was Jake paid in advance?

(A) 0.8b
(B) 1.1b
(C) 1.2b
(D) 10b
(E) 11b

Please help with the shortest approach.

(A) 0.8b
(B) 1.1b
(C) 1.2b
(D) 10b
(E) 11b

SidR · Accepted Answer

Got it thanks a lot.

(a+b)/1.2t = (a-b)/t --> 0.2a=22b --> a=11b

Just one question, in such type of word problems if the equation immediately does not pop up in the head, is it advisable to plug in the variables?

GyMrAT · Answer

The shortest approach will be to assume the # of hours of work required.

Lets assume the job required 10 hours of work for a pay of X dollar.

So Ryan worked for 10 hours for X dollars.

& Jake worked for 20% more time than Ryan, hence Jake worked for 12 hours for X dollars.

Now Ryan gave Jake "b" dollars, which made their hourly pay equal.

So, we get (X-b)/10 = (X+b)/12

Solving it for X we get X = 11b.

Answer E.

Thanks,
GyM

Bunuel · Answer

It's a copy of the following Official guide question: https://gmatclub.com/forum/john-and-mar ... 44782.html

EgmatQuantExpert · Answer

Plugging in numbers in word problems can be a good approach sometimes, provided you do that in a smart way. If you have gone through the solutions of the question referred by Bunuel, you must have understood that just assuming any number may worsen the situation, rather than help in solving.

Also, another risk you may face – plugging in numbers may not give you exhaustive list of solutions every time. Some cases you may need to check all the options, even if one option gets satisfied with your plugged-in value.

If you can do it smartly, then consider it as an alternate way only.

push12345 · Answer

After giving and taking b dollars

(a+b)/1.2t = (a-b)/t

--> 0.2a=22b 
--> a=11b

Posted from my mobile device

ScottTargetTestPrep · Answer

We can assume each was given 110 dollars for the job. Furthermore, we can assume that Ryan worked 10 hours and Jake worked 12 hours. Thus, the hourly wage, which must be equal for both, should be:

(110 + 110)/(10 + 12) = 220/22 = $10

Therefore, we see that Ryan should give Jake $10 so that Ryan would have $100 (notice that 10 x $10 = $100) and Jake would have $120 (notice that 12 x $10 = $120).

We see that a = 110 and b = 10, so a = 11b.

Answer: E

hero_with_1000_faces · Answer

Setting up equation is the only challenge here, but equations can be setup only when the question is understood and absorbed clearly. great question.

Kinshook · Answer

Given: Jake and Ryan worked together on a job for which they were each paid a dollars in advance. 
Asked: If Jake spent 20% more time working on the job than Ryan did, and Ryan gave Jake b dollars, so that their hourly wages were equal, then, in terms of b, how much was Jake paid in advance?

Jake spent 1.2 times time that Ryan spent
If their hourly wages were equal, Jake will receive 1.2 times amount that Ryan recieved

After all transactions Jake had = a + b dollars
After all transactions Ryan had = a - b dollars

a + b = 1.2 (a-b) = 1.2a - 1.2b
.2a = 2.2b
a = 11b

IMO E

laborumplaceat · Answer

E is correct 
amount payed in advance = a
time worked by J = 1.2t
time worked by R = t
Same hourly wage means that a-b= (a+b)/1.2
a = 11b

Jake and Ryan worked together on a job for which they were each paid

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Jake and Ryan worked together on a job for which they were each paid

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