hi...

you would see such Q more frequently in CAT

but let's solve it.

they were to lose thrice the amount of wages of work that was left ....
so if they lost \(\frac{3}{8}\) of work, they did not do \(\frac{3}{8} * \frac{1}{3} = \frac{1}{8}\) of work

In other words they did only \(1-\frac{1}{8} = \frac{7}{8}\) of work
if they do 7/8 of work in 14 days, they will do complete job in 14*8/7 = 16 days..

David's one day work = \(\frac{1}{16}-\frac{1}{80} = \frac{5-1}{80}=\frac{4}{80}=\frac{1}{20}\)
so david does it in 20 days

A
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Since they lost 3/8 of the amount that they would have together received had they completed the job on time and they actually forfeited thrice the amount of wages corresponding to the unfinished, we can relate these two quantities as: ⅜ = 3x, and so x = ⅛, which means that they only had 1/8 of the job unfinished. In other words, they finished 7/8 of the job.

We can let n = the number of days David would take to complete the work alone. We are given that Sam would take 80 days to complete the work alone; thus, his rate would be 1/80, and David’s rate would be 1/n. Since they both worked 14 days, and they finished 7/8 of the job, we can create the following equation:

14 x 1/80 + 14 x 1/n = 7/8

14/80 + 14/n = 7/8

Multiply the equation by 80n we have:

14n + 1120 = 70n

1120 = 56n

n = 1120/56 = 20

Answer: A
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