Question

During one of his adventure, Chacha chaudhary got trapped in an underground cave which was sealed two hundred year back. The air inside the cave was poisonous, having some amount of carbon monoxide in addition to $O_2$ and $N_{2.}$ Sabu, being huge could not enter into the cave , so in order to save chacha choudhary be started sucking the poisonous air out of the cave by mouth/ Each time, he filled his lunge with cave air and exhaled it out in the surroundings. In the mean time fresh air from surrounding effused into the cave till the pressure was again one atmosphere. Each time Sabu sucked out some air, the pressure in the cave dropped to half of its initial value of one atmosphere. If lthe safe level of CO in the atmosphere is less than 0.001 per by volume how many times does Sabu need to such out air in order to save Chacha Chaudhary.

Answer 1

Each time air is exhaled, the percentage by volume of CO reduces to half as fresh air mixes with contaminated air.
The final percentage by volume is less than or equal to 0.001%
Let the original percentage by volume of CO be 10%.
Hence, $\frac{10}{2^n}=0.001$
or $n=13$.
Hence, sabu should exhale air by 13 times.