# Difficult Time and Work Solved QuestionAptitude Discussion

 Q. A man takes 20 days to reach the point $B$ under normal circumstances. But, due to the increasingly hostile weather conditions the distance they travel every day reduces by $20%$. In how many days would the man reach the point $B$, taking into consideration weather conditions?
 ✖ A. 25 ✖ B. 50 ✖ C. 100 ✔ D. None of these

Solution:
Option(D) is correct

Let the total distance to be covered be $d$

On each day under normal weather conditions they travel $\dfrac{d}{20}$of the distance.

On $1^{st}$ day they would travel$=\dfrac{d}{20}$

On $2^{nd}$ day they would travel $=0.8\times \dfrac{d}{20}$

On $3^{rd}$ day they would travel$=0.8\times \dfrac{0.8\times d}{20}$

Let he will reach the point $B$ in $n^{th}$ day

$\Rightarrow \dfrac{d}{20}+0.8\dfrac{d}{20}+0.8^2\dfrac{d}{20}+...0.8^n\dfrac{d}{20}=d$

$\Rightarrow \dfrac{d}{20}\times \dfrac{-(0.8)^n+1}{-0.8+1}=d$

$\Rightarrow 1-(0.8)n$

$=4(0.8)^n$

$=-3$

Since $(0.8)6 n>0$, thus it is never equal to -3

The man will never reach the point B.