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 containerSolution
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
40    42    87    266    ?     5366
14Â Â 16Â Â Â 20Â Â Â 15Â Â 25Â Â Â Â 13Â Â Â 29Â Â Â 9Â Â Â 32Â Â Â 6
...There are three series given below which are following with the same pattern.
Series I: 21, 44, 135, 544, 2725
Series II: 14, B, C, D, E
112    162    199    ?     242    252
...2556   636    156    ?    6
98    219    75    244    ?    273
62 90 122 158 198 ?
50 62 ? 96 126 138
...59, 170, 301, 452, ?, 814
35 36 68 207 836 4205
...
Relevant for Exams:
