$A$ mixture of $30 \ L$ contains milk and water in the ratio of $7:3$. How much water should be added to it so that the ratio of milk and water becomes $3:7$? (in $L$)

An alloy contains copper,zinc and nickel in the ratio of $5: 3: 2$. The quantity of nickel in $kg$ that must be added to $100\, kg$ of this alloy to have the new ratio $5: 3: 3$ is

$A$ vessel of $160 \text{ litres}$ is filled with milk and water. $70 \%$ of milk and $30 \%$ of water is taken out of the vessel. After this task,it is found that the vessel is now filled by $55 \%$ of its original total quantity. What is the original quantity of milk and water in the vessel respectively?

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 $B\,?$

Aditya and Sanjay started a business investing $45000$ and $30000$ respectively. What will be the ratio between their profit?

How much water must be added to a vessel which contains $80$ litres of milk at a cost price of ₹ $3.5/litre$ so that the cost of the milk reduces to ₹ $2/litre$? (in litres)