$A$ can contains a mixture of two liquids $A$ and $B$ in the ratio $7:5$. When $9\,L$ of mixture is drained off and the can is filled with $B$,the ratio of $A$ and $B$ becomes $7:9$. How many litres of liquid $A$ was contained by the can initially?

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

Find the ratio in which rice at ₹ $7.20/kg$ should be mixed with rice at ₹ $5.70/kg$ to produce a mixture worth ₹ $6.30/kg$.

$A$ man has given ₹ $300000$ as a loan. He lent some of his capital to Ajay at an interest rate of $20 \%$ per annum and the rest to Ramesh at an interest rate of $12 \%$ per annum. At the end of one year,he received $17 \%$ of his total capital as interest. How much did he lend to Ajay? (in ₹)

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 $B\,?$

$A$ sugar solution of $3$ $litre$ contains $60 \%$ sugar. One litre of water is added to this solution. Then the percentage of sugar in the new solution is (in $\%$)