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A man builds $\dfrac{1}{8}$ th part of wall each day but $20\%$ of the wall built on each day falls down. In how many days will the construction of the wall be finished?

My doubt particularly is why we are choosing the unit of work here. $\dfrac{1}{8}$th is interpreted as whole number. Why is that so? Also here the problem is more difficult than it seems. A detailed theory about this is most welcome.

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    $\begingroup$ Why do you say that 1/8 is treated as a whole number here? $\endgroup$
    – David
    Jun 4, 2021 at 14:40
  • $\begingroup$ The instructor took the work as 80 units. $\endgroup$ Jun 4, 2021 at 14:55
  • $\begingroup$ It may help to walk through this building process one day at a time. On day 1, the builder completes $\frac18$ of the wall. At the end of day 1, $20\%$ or $\frac2{10}$ of that wall breaks down, which means $\frac18\times\frac2{10}=\frac1{40}=2.5\%$ of the wall is undone, leaving the builder with $\frac18-\frac1{40}=\frac5{40}-\frac1{40}=\frac4{40}=\frac1{10}=10\%$ of the wall completed. What happens on day 2? $\endgroup$
    – user170231
    Jun 4, 2021 at 14:55
  • $\begingroup$ Up to 9 th day it is predictable. What about the 10 th day? $\endgroup$ Jun 4, 2021 at 15:21
  • $\begingroup$ On any given day, $\frac18$ of the wall is built, and $20\%$ of what was completed on that day is destroyed. So the builder is completing the same amount each day. $\endgroup$
    – user170231
    Jun 4, 2021 at 15:39

1 Answer 1

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Well, if $\frac{1}{8}$ of the wall is built, but $20$%, or $\frac{1}{5}$, of that falls down, then each day, the man builds $\frac{4}{5} \cdot\frac{1}{8} = \frac{4}{40} = \frac{1}{10}$ of the wall in a day. So the wall will be completed in $10$ days.

I hope this helped!

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