Pencils at $Rs. 4.20$ per dozen are mixed with pencils at $Rs. 5.40$ per dozen in the ratio $3:5$. Find the price per dozen of the mixture (in $Rs.$).

$A$ person has ₹ $5000$. He invests a part of it at $3 \%$ per annum and the remainder at $8 \%$ per annum simple interest. His total income in $3$ years is ₹ $750$. Find the sum invested at different rates of interest (in ₹).

Nine litres of water are drawn from a container full of water and it is then filled with milk. Nine litres of mixture are drawn and the container is again filled with milk. The ratio of the quantity of water now left in the container to that of the milk in it is $16:9$. How much liquid does the container hold? (in $litres$)

$A$ tub contains a mixture of two liquids $P$ and $Q$ in the ratio of $4:1$. When $10 \, L$ of the mixture is taken out and $10 \, L$ of liquid $Q$ is poured into the tub,the ratio becomes $2:3$. How many litres of liquid $P$ were contained in the tub initially?

In what proportion must sugar of $Rs. 17$ per $kg$ be mixed with sugar of $Rs. 29$ per $kg$ to make a mixture of $Rs. 20$ per $kg$?

$A$ person has a chemical costing $Rs. 25$ per $litre$. In what ratio should water be mixed in the chemical so that by selling the mixture at $Rs. 20$ per $litre$,he may get a profit of $25\%$?