$15$ litres of mixture contains $20 \%$ alcohol and the rest water. If $3$ litres of water be mixed with it,the percentage of alcohol in the new mixture would be:

Divide ₹ $1,000$ among $P, Q,$ and $R$ such that $P$ gets $\frac{2}{3}$ of $Q$'s share and $R$ gets $\frac{5}{3}$ of $Q$'s share. What is the share of $Q$?

If $33 \%$ of $A$ is equal to $55 \%$ of $B$,then find the ratio of $A$ and $B$.

$Rs. 2186$ is distributed among $A$,$B$,and $C$. If the money given to them is decreased by $Rs. 26$,$Rs. 28$,and $Rs. 32$ respectively,then the ratio of their shares becomes $9: 13: 8$. What is the amount (in $Rs.$) given to $A$?

There is $1000 \, \text{litres}$ of milk in a pot. $100 \, \text{litres}$ of milk is taken out and the same amount of water is poured into it. Again, $200 \, \text{litres}$ of the mixture is taken out and the same amount of water is poured into it, and finally, $400 \, \text{litres}$ of the mixture is taken out and the same amount of water is poured into it. What is the amount of milk in the resulting mixture?

The ratio of the present ages of $R$ and $S$ is $11:17$. $11$ years ago,the ratio of their ages was $11:20$. What is $R$'s present age (in years)?