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

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

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

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

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

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...

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