A vessel contains a mixture of o2 and n2. The quantity
of o2 is 16% of total mixture. Some quantity of
mixture taken out from it and replaced by n2. This
process is repeated once more. Now the quantity of
o2 is 9% of total mixture. If total quantity of mixture
was 8 lt, then find the quantity of mixture which
is taken out.
Answers
Given : A vessel contains a mixture of o2 and n2.
The quantity of o2 is 16% of total mixture.
Some quantity of mixture taken out from it and replaced by n2.
This process is repeated once more.
Now the quantity of o2 is 9% of total mixture
total quantity of mixture was 8 lt
To Find : ., then find the quantity of mixture which is taken out.
Solution:
Initial = 8 litre
o2 = (16/100)8 = 1.28 litre
n2 = 8 - 1.28 = 6.72 litre
let say x taken out
then o2 taken out = (16/100)x = 0.16x
so o2 let = 1.28 - 0.16x litre
again x litre taken out
o2 taken out = x*(1.28 - 0.16x)/8
= 0.16x - 0.02x²
o2 = 1.28 - 0.16x - ( 0.16x - 0.02x²)
= 0.02x² - 0.32x + 128
o2 = 9 % = (9/100)8 = 0.72 litre
0.02x² - 0.32x + 128 = 0.72
=> 0.02x² - 0.32x + 0.56 = 0
=> 2x² - 32x + 56 = 0
=> x² - 16x + 28 = 0
=> (x - 2)(x - 14) = 0
=> x= 2 or 14
Solution was 8 litre hence 14 litre not possible
so x = 2
quantity of mixture which is taken out. = 2 litre
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