Working alone Jerry can complete a work in 6 minutes. Working alone, A

Question

Working alone Jerry can complete a work in 6 minutes. Working alone, Adam can complete a work in 8 minutes. Working together, Jerry leaves the work after 2 minutes. How long will it take Adam to complete the work?

A. 2 minutes
B. 3 minutes
C. 10/3 minutes
D. 5 minutes
E. 10 minutes

A. 2 minutes
B. 3 minutes
C. 10/3 minutes
D. 5 minutes
E. 10 minutes

Chethan92 · Answer

LCM of 6 and 8 is 24 units = Total work to be done.
Jerry can do 4 units per minute.
Adam can do 3 units per minute.
Working together they complete 7 unit per minute.

Working for 2 minute they complete 14 units. Pending is 24-14 = 10 units.
Adam will complete in 10/3 minutes.

C is the answer

Posted from my mobile device

Archit3110 · Answer

GMATinsight  :

Sir, I solved the question using below method , but I am not able to get option C which is correct answer ...

Rate of jerry = x/6 and rate of Adam= x/8
combined rate : x/6+x/8 = 7x/24 and work would be x.24/7
work done in 2 mins: x.(7/24) * 2 = 7x/12 
 work left =x - 7x/12 = 5x/12
time Adam will take : work = rate * time
5x/12=x/8* time

time : 10/3 IMO C

baru · Answer

==> Adam takes 8 min / work . So , 5X/12 work is done in ==> 5(8)/12 = 10/3

Archit3110 · Answer

baru thanks a lot .. such a stupid error i did in the end ...

.. thanks for highlighting the error..

GMATinsight · Answer

This question can be solved in two ways

Method 1:  
Jerry's 1 minute work = 1/6
Adam's 1 minute work = 1/8

Work done by Jerry in 2 minutes = 2/6 = 1/3
Remaining work = 1 - (1/3) = 2/3

Adam can finish (1/8) work in 1 minute
Adam will finish (2/3) work in (2/3)*8 = 16/3 minutes

But Adam worked for first two minutes with Adam hence

Additional time for which Adam worked alone = 16/3 - 2 - 10/3

Answer: Option C

Method 2

Let work = LCM of 8 and 6 = 24 units

Jerry's 1 minute work = 24/6 = 4 units
Adam's 1 minute work = 24/8 = 3 units

Jerry's work done in 2 minutes = 2*4 = 8 units

Remaining work = 24 - 8 = 16 units

Time taken by Adam to finish 16 unit work = 16/3 minutes

Extra time that Adam worked alone for = 16/3 - 2 = 10/3 minutes

Answer: Option C

generis · Answer

Another way, not hard: two stages. Use combined rate in the first stage.
J's rate:  \frac{1}{6} 
A's rate:  \frac{1}{8} 
Combined rate _{(J+A)} : (\frac{1}{6}+\frac{1}{8})=\frac{14}{48}=\frac{7}{24}

They work together for 2 minutes. Then Jerry leaves.

(1)  Stage 1: Work completed together?
 R_{(J+A)}*T_{mins}=W 
 (\frac{7}{24}*2)=\frac{14}{24}W=\frac{7}{12}W

Together they finish  \frac{7}{12}  of work. Job = 1
So the work remaining for Adam is
 (1-\frac{7}{12})=(\frac{12}{12}-\frac{7}{12})=\frac{5}{12}W

(2)  Stage 2: Time required for Adam to finish the work?
 R_{A}*T_{mins}=W_{remaining}

\frac{1}{8}*T_{mins}=\frac{5}{12}

T_{mins}=(\frac{5}{12}*\frac{8}{1})=\frac{40}{12}=\frac{10}{3}  minutes*

Answer C

*In solving for  T  by clearing LHS, the underlying operation is just  T=\frac{W}{R} , thus:
 \frac{1}{8}*T_{mins}=\frac{5}{12} 
 T_{minutes}=\frac{W}{R_{A}}=\frac{(\frac{5}{12})}{(\frac{1}{8})}=(\frac{5}{12}*\frac{8}{1})=\frac{40}{12}=\frac{10}{3}

AdityaHongunti · Answer

All the above solutions are helpful and should be solved in that way when YOU HAVE TIME...
 when you are running out of time...US THIS 
i used the answer choices to increase my probability of answering the question right
we are given individual rates ... Rate of jerry > rate of adam
working alone adam complete the ENTIRE work in 8 minutes os with the help of jerry he will complete it in even less time
option E is gone

as we know rate of j > rate of adam and jerry works for 2 minutes and then leaves then for the rest of the part adam has to work...as adam is slower than jerry it is impossible for him to complete the remaining job in 2 mins
option A is gone

we have 6 and 8 in the question... 6 is a multiple of 2 and 3 ... division by 3 of a non multple of three ends in a non terminating decimal ...so the adddition and interpolation of fraction ending up in integer value when reversed for time is very less

this eliminate B and D...

bumpbot · Answer

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