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    Question

    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
    A loses entire hydrogen gas in 3 days Correct Answer Incorrect Answer
    B loses entire hydrogen gas in 10 days Correct Answer Incorrect Answer
    C loses 150 liters of hydrogen gas in 10 days Correct Answer Incorrect Answer
    D possesses at least 150 liters of hydrogen gas on 100th day Correct Answer Incorrect Answer

    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

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