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21 Mar 2023, 06:05
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
66% (03:09) correct
34%
(03:18)
wrong
based on 237
sessions
History
Date
Time
Result
Not Attempted Yet
Jeff started working alone on a project at 7:00 am. At the end of his 12-hour shift, which includes a 1-hour lunchtime, he completed a portion of his work. He starts again the next day at the same time; however, he now has the help of his colleague, Ken, who helps him to wrap up the project by 3.30 pm. Since he was able to finish the job before his shift ended, Jeff and Ken did not take the lunch break. If Ken, works on the same project at his constant rate and finishes the work in 15 hours, how much time will Jeff take to complete the project if he works alone?
(A) 20
(B) 25
(C) 30
(D) 40
(E) 45
(A) 20
(B) 25
(C) 30
(D) 40
(E) 45
21 Mar 2023, 13:02
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ChandlerBong
At the end of the entire project -
Jeff has worked for 11 + 8.5 = 19.5 hours
Ken has worked for 0 + 8.5 = 8.5 hours
The question states that Ken can complete 100% of the work in 15 hours. Percentage of work contributed by Ken in 8.5 hours =
\(\frac{100 }{ 15 * 8.5} = \frac{100 * 85 }{ 15 * 10} = \frac{170}{3}\)
Percentage of work contributed by Jeff = \(100 - \frac{170}{3} = \frac{130}{3}\)
If Jeff can do \(\frac{130}{3}\) % of work in 19.5 hours, the time taken by him to complete 100% of the work =
\(\frac{19.5 }{ 130 } * 3 * 100\) = \(\frac{195 }{ 10* 130 } * 3 * 100\) = 15 * 3 = 45 hours
Option E
01 Sep 2024, 03:15
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ChandlerBong
Assuming efficiencies as J and K for both jeff and ken.
Jeff starts working from 7:00 am on both days and ken was there with him on 2nd day. and similar amount of work ken completes in 15 Hrs
Therefore,
\(11J + \frac{17}{2}*(J+K) = 15K\)
on solving,
we get, \(\frac{J}{K} = \frac{1}{3}\)
this is ratio of efficiency which is reciprocal of ratios of time taken by them.
Therefore \(Tj = 3*Tk \)
Tj = Time taken by Jeff if working alone. and Tk = Time taken by ken if working alone.
Tj = 3*15 = 45 Hrs
Answer is E.
