Jane and Ashley take 20 days and 40 days respectively to

Assume Jane and Ashley worked together for x days without considering the 8 day leave of Jane. They would have completed \(x(\frac{1}{40} + \frac{1}{20})\) of the total work in those days. In the period when Jane took a 8 day leave, Ashley worked alone. So Ashley worked alone for 8 days. He would have completed \(\frac{8}{40}\) th of the total work. The work finished before Jane started working alone, is \(x(\frac{1}{20} + \frac{1}{40}) + \frac{8}{40}\). This is equal to \(\frac{4}{5}\) of the total work as in the period when Jane was working alone which is 4 days, she would have completed \(\frac{4}{20}\) or \(\frac{1}{5}\) of the work. Previously done work is therefore \(\frac{4}{5}\).

\(x(\frac{1}{40} +\frac{1}{20}) +\frac{8}{40} = \frac{4}{5}\)

We have x = 8

Add to this the 8 days when Ashley worked alone and the 4 days when Jane worked alone. The total is 8+8+4=20 days.

I generally use take a constant (LCM) and a production example for this kind of questions.

Assuming that Jane and Ashley's work is production of certain number of Toys

In 20 days Jane completes making certain number of Toys and the same number of Toys takes 40 days for Ashley to complete, so we take the LCM (Lowest common Multiple) which would be the target work = 80 toys to complete

From above assumption we know that Jane completes 4 toys / day as in 80/20 days

And Ashley completes 2 toys / Day as in 80/40 days

Now if both worked without any break they would take 80/4+2 days to complete which is 13.333 days, so that eliminates choice (A) = 10 days

Now plugging in choices, B - Jane completes (15-8)*4 = 28
Ashley completes 15*2 =30
Total work in 15 days with 8 days break by Jane = 28+30 = 58 toys
Jane works for 4 days on her own = 4*4 = 16 toys
So in 15 days ( both Jane & Ashley)+ 4 days(only Jane) they complete 58+16 =74 toys, 6 short of the target of 80

Plug in choice C - Ashley completes 16*2= 32 toys
Jane completes 8*4 = 32 toys
Total in 16 days = 64 toys
Jane takes 4 days on her own, 4*4 = 16 toys
So in 16 days ( both Jane & Ashley)+ 4 days(only Jane) they complete = 64+16 = 80 toys which is the target.

Ans : E

How could you reach to 4/5th of the total work please explain in detail

Jane’s rate is 1/20, Ashley’s rate is 1/40, and their combined rate is 1/20 + 1/40 = 2/40 + 1/40 = 3/40. We can let n = the number of days they actually worked together and create the equation:

Together + Ashley alone + Jane alone = 1 job

(3/40)n + (1/40)8 + (1/20)4 = 1

3n/40 + 8/40 + 4/20 = 1

Multiplying by 40 we have:

3n + 8 + 8 = 40

3n = 24

n = 8

So it took 8 + 8 + 4 = 20 days to complete the project.

Answer: E

We are told that Jane had to work FOUR extra days to make up for the work-loss incurred because of the EIGHT days leave that she took while working together with Ashley.We can thus conclude that, while determining how many days they would need to complete the project (Scheduled Time for Completion or STC), Jane and Ashley had factored in a four-day leave for Jane.
If we denote STC by 'x', the plan was that Jane would work for (x-4) days and Ashley 'x' days. So as per the STC, Jane would have done (1/20)*(x-4)th of the work and Ashley (1/40)*(x)th.

(1/20)*(x-4) + (1/40)*x = 1....> x=16

Scheduled time for completion of project = 16 days
Actual time taken to complete project = 16+4=20 days.
ANS: E

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