Two vessels $A$ and $B$ contain milk and water mixed in the ratio $8: 5$ and $5: 2,$ respectively. The ratio in which these two mixtures should be mixed to get a new mixture containing $69 \frac{3}{13} \%$ milk is

$49 \ kg$ of blended tea contains Assam and Darjeeling tea in the ratio $5:2$. The quantity of Darjeeling tea to be added to the mixture to make the ratio of Assam to Darjeeling tea $2:1$ is..........$kg$.

In what proportion must water be added to spirit to gain $20 \%$ by selling it at the cost price (in $:5$)?

$300$ $gm$ of sugar solution contains $40 \%$ sugar. How much sugar (in $gm$) should be added to make the concentration $50 \%$ in the solution?

In what ratio must a grocer mix two varieties of tea worth $Rs. 60$ per $kg$ and $Rs. 65$ per $kg$ so that by selling the mixture at $Rs. 68.20$ per $kg$ he may gain $10\%$?

There are two vessels $A$ and $B.$ Vessel $A$ contains $40$ $litres$ of pure milk and vessel $B$ contains $22$ $litres$ of pure water. From vessel $A,$ $8$ $litres$ of milk is taken out and poured into vessel $B.$ Then,$6$ $litres$ of the mixture (milk and water) is taken out from vessel $B$ and poured into vessel $A.$ What is the ratio of the quantity of pure milk in vessel $A$ to the quantity of pure water in vessel $B\,?$