A container is filled with 300 liters of hydrogen gas. The first day it loses 100 liters of hydrogen gas and everyday it loses one-third of the volume it lost in the previous day. Then the container

Solution

First-day gas lost = 100 L Second day, gas lost = 100/3 = 33.33L Third day, gas lost = 33.33/3 = 11.11 L = 100/3² L Fourth day, gas lost = 11.11/3 = 3.7L = 100/3³ L Fifth day, gas lost = 3.7/3 = 1.23L Sixth day, gas lost = 1.23/4 = 0.41L Seventh-day, gas lost = 0.41/3 = 0.137L Eighth day, gas lost = 0.137/3 = 0.045L Ninth day, gas lost = 0.045/3 = 0.015L Tenth day, gas lost = 0.015/3 = 0.005L Total gas loss is equal to 149.982L On 100Th day =  100/3⁹⁹ L Total lost in 100 day = 100 + 100/3 + 100/3² + .... + 100/3⁹⁹ = 100 [(1+ 1/3 + 1/3² + 1/3³)/(1-(1/3))] = 150 [1 - (1/3¹⁰⁰)] ∴ Possesses at least 150 litres of hydrogen gas on 100th day