(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

$A$ shopkeeper bought $20 \ kg$ of onions at $Rs. 6.50$ per $kg$ and $30 \ kg$ of onions at $Rs. 7$ per $kg$. He sold the mixture at a total profit of $Rs. 60$. At what price per $kg$ did he sell the mixture of onions? (in $Rs.$)

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In what ratio must water be mixed with milk to gain $16 \%$ on selling the mixture at cost price?

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$A$ trader has $50 \text{ kg}$ of rice,a part of which he sells at $10 \%$ profit and the rest at $5 \%$ loss. He gains $7 \%$ on the whole. What is the quantity sold at $10 \%$ gain and $5 \%$ loss? (in $\text{kg}$)

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Nikita bought $30 \text{ kg}$ of wheat at the rate of $Rs. 9.50$ per $\text{kg}$ and $40 \text{ kg}$ of wheat at the rate of $Rs. 8.50$ per $\text{kg}$ and mixed them. She sold the mixture at the rate of $Rs. 8.90$ per $\text{kg}$. Her total profit or loss in the transaction was:

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Two vessels contain milk and water in the ratio $3:2$ and $7:3$. Find the ratio in which the contents of the two vessels have to be mixed to get a new mixture in which the ratio of milk and water is $2:1$.

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$A$ shopkeeper bought $20 \ kg$ of onions at $Rs. 6.50$ per $kg$ and $30 \ kg$ of onions at $Rs. 7$ per $kg$. He sold the mixture at a total profit of $Rs. 60$. At what price per $kg$ did he sell the mixture of onions? (in $Rs.$)

In what ratio must water be mixed with milk to gain $16 \%$ on selling the mixture at cost price?

$A$ trader has $50 \text{ kg}$ of rice,a part of which he sells at $10 \%$ profit and the rest at $5 \%$ loss. He gains $7 \%$ on the whole. What is the quantity sold at $10 \%$ gain and $5 \%$ loss? (in $\text{kg}$)

Nikita bought $30 \text{ kg}$ of wheat at the rate of $Rs. 9.50$ per $\text{kg}$ and $40 \text{ kg}$ of wheat at the rate of $Rs. 8.50$ per $\text{kg}$ and mixed them. She sold the mixture at the rate of $Rs. 8.90$ per $\text{kg}$. Her total profit or loss in the transaction was:

Two vessels contain milk and water in the ratio $3:2$ and $7:3$. Find the ratio in which the contents of the two vessels have to be mixed to get a new mixture in which the ratio of milk and water is $2:1$.

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