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 $Rs.$).

$8$ litres of water is added to $32$ litres of a solution containing $20 \%$ of alcohol in water. What is the approximate concentration of alcohol in the solution now? (in $\%$)

$A$ merchant mixes three varieties of rice costing $Rs. 20$ per $kg$,$Rs. 24$ per $kg$,and $Rs. 30$ per $kg$ and sells the mixture at a profit of $20\%$ at $Rs. 30$ per $kg$. How many $kgs$ of the second variety will be in the mixture if $2$ $kgs$ of the third variety is there in the mixture?

$400 \, gm$ of salt solution has $40 \%$ salt in it. How much salt should be added to make the concentration $50 \%$ in the solution?

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

How many kilograms of sugar costing $Rs. 9$ per $kg$ must be mixed with $27\, kg$ of sugar costing $Rs. 7$ per $kg$ so that there may be a gain of $10\%$ by selling the mixture at $Rs. 9.24$ per $kg$?