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23 May 2022, 03:45
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
78% (03:07) correct
22%
(03:16)
wrong
based on 215
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A alone can finish a piece of work 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 3 days A is called back and he finishes the remaining 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 the amount of work that they do.
(A) $588, $420
(B) $654, $350
(C) $672, $338
(D) $675, $330
(E) $679, $330
(A) $588, $420
(B) $654, $350
(C) $672, $338
(D) $675, $330
(E) $679, $330
Updated on: 23 May 2022, 07:45
Originally posted by ThatDudeKnows on 23 May 2022, 06:41.
Last edited by ThatDudeKnows on 23 May 2022, 07:45, edited 1 time in total.
Last edited by ThatDudeKnows on 23 May 2022, 07:45, edited 1 time in total.
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Bunuel
We are tasked with figuring out to what portion of the $1008 each of the employees is entitled. If we can determine how much A is entitled to, that will tell us how much B is entitled to. Or, if we can determine how much B is entitled to, that will tell us how much A is entitled to. We can choose whichever is easier to solve for and that will tell us about the other!! Solving for A would take more steps than solving for B, so let's just do B.
B works for a total of 5 days. He could have finished the job alone in 12 days. So, B did 5/12 of the job and is therefore entitled to 5/12 of the pay. 5/12 of $1008 is $420.
Answer choice A.
ThatDudeKnowsRates
23 May 2022, 07:38
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A alone can finish a piece of work 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 3 days A is called back and he finishes the remaining 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 the amount of work that they do.
(A) $588, $420
(B) $654, $350
(C) $672, $338
(D) $675, $330
(E) $679, $330
IMO A
the amount is distributed in the ratio of the amount of work that they do
to get the amount of work done = We need to find the number of days they (A and B) are working and multiply it with the rate of their work
Number of Days A worked for at First =2
Number of Days B worked for at First = 2+3 =5
Work done by A+B in the first 2 days when they were working together = (1/6+1/12)*2 = 1/2
Work left to do after first 2 days = 1/2
Work done by B alone in the next 3 days = 3*(1/12) = 1/4
Work left to do after 5th Day when A is called back to work alone = 1/4
Time taken by A to finish 1/4 of the work is = (1/4)/(1/6) = 1.5 Days
so 1.5 days A is working alone after the 5th day of Work
lets make it into a table :
_______________________
Days : Work Done by
______________________
Day 1-2 : A+B
Day 3-5 : B
Day 6-7.5 : A
Total number of days A has worked = 2+1.5 = 3.5 days
Total number of days B has worked = 2+3 = 5 days
Work done by A : work done by B
3.5 *(1/6)*1008 : 5*(1/12)*1008
588 : 420
(A) $588, $420
(B) $654, $350
(C) $672, $338
(D) $675, $330
(E) $679, $330
IMO A
the amount is distributed in the ratio of the amount of work that they do
to get the amount of work done = We need to find the number of days they (A and B) are working and multiply it with the rate of their work
Number of Days A worked for at First =2
Number of Days B worked for at First = 2+3 =5
Work done by A+B in the first 2 days when they were working together = (1/6+1/12)*2 = 1/2
Work left to do after first 2 days = 1/2
Work done by B alone in the next 3 days = 3*(1/12) = 1/4
Work left to do after 5th Day when A is called back to work alone = 1/4
Time taken by A to finish 1/4 of the work is = (1/4)/(1/6) = 1.5 Days
so 1.5 days A is working alone after the 5th day of Work
lets make it into a table :
_______________________
Days : Work Done by
______________________
Day 1-2 : A+B
Day 3-5 : B
Day 6-7.5 : A
Total number of days A has worked = 2+1.5 = 3.5 days
Total number of days B has worked = 2+3 = 5 days
Work done by A : work done by B
3.5 *(1/6)*1008 : 5*(1/12)*1008
588 : 420
