Question

The pollution in a normal atmosphere is less than $0.01\%$. Due to the leakage of gas from a factory the pollution is increased to $20\%$. If every day $80\%$ of the pollution is neutralised. In how many days the atmosphere will be normal.

Answer 1

The pollution has been increased to $20$.

Every day, $80$ pollution is being neutralized, so only $20$ of the total pollution remains the next day.

Let $x$ days be needed to bring back the pollution to normal.
Thus, $(0.2{)}^x\times 0.2<0.0001$

$\Rightarrow (0.2{)}^x<0.0005$

We have $(0.2{)}^4=0.0016$ and $(0.2{)}^5=0.00032$ (can guess the value $x$ on the basis of number of digits after decimal point too)

Hence,minimum of 6 days will be required to bring the pollution back to normal.