(A) Let the amount of mixture released each time be $y \text{ litres}$.The initial volume of oxygen is $16 \%$ of $8 \text{ litres}$,which is $0.16 \t

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(A) Let the amount of mixture released each time be $y \text{ litres}$.The initial volume of oxygen is $16 \%$ of $8 \text{ litres}$,which is $0.16 \times 8$.After the first replacement,the remaining oxygen is $8 \times 0.16 \times (1 - y/8)$.After the second replacement,the remaining oxygen is $8 \times 0.16 \times (1 - y/8)^2$.According to the problem,the final oxygen content is $9 \%$ of the total volume $(8 \text{ litres})$,so:$8 \times 0.16 \times (1 - y/8)^2 = 0.09 \times 8$$(1 - y/8)^2 = 0.09 / 0.16$$(1 - y/8)^2 = (0.3 / 0.4)^2 = (3/4)^2$$1 - y/8 = 3/4$$y/8 = 1 - 3/4 = 1/4$$y = 8 / 4 = 2 \text{ litres}$.

Competitive Quantitative Aptitude Mixture and Alligation Mixture and Alligation

Medium

$A$ cylinder which has the capacity of $8 \text{ litres}$ contains a mixture of oxygen and nitrogen. The volume of oxygen in the cylinder is $16 \%$ of the total volume. $A$ few litres of the mixture is released and an equal amount of nitrogen is added. Then,the same amount of the mixture as before is released and replaced by nitrogen for the second time. As a result,the oxygen content becomes $9 \%$ of the total volume. Find the amount of mixture released each time (in litres).

A
$2$
B
$2.5$
C
$1$
D
$0.5$

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Mixture and Alligation

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Mixture and Alligation

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How many kg of sugar costing ₹ $11.70/kg$ must be mixed with $24$ $kg$ of sugar costing ₹ $8.1/kg$ so that there may be a gain of $15 \%$ by selling the mixture at ₹ $9/kg$? (in $kg$)

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