Sourav purchased $30 \text{ kg}$ of rice at the rate of $₹ 10$ per $\text{kg}$ and $35 \text{ kg}$ at the rate of $₹ 11$ per $\text{kg}$. He mixed the two. At what price per $\text{kg}$ should he sell the mixture to make a $30\%$ profit in the transaction?

In what ratio must a grocer mix two varieties of pulses costing ₹ $15$ and ₹ $20$ per $kg$ respectively so as to get a mixture worth ₹ $16.5/kg$?

Gold is $19$ times as heavy as water and copper is $9$ times. In what ratio should these metals be mixed so that the mixture may be $15$ times as heavy as water?

$300\, gm$ of salt solution has $40 \%$ salt in it. How much salt should be added to make it $50 \%$ in the solution? (in $gm$)

$A$ cylinder which has the capacity of $8 \text{ litres}$ contains a mixture of oxygen and nitrogen. The volume of oxygen in the cylinder is $16 \%$ of the total volume. $A$ few litres of the mixture is released and an equal amount of nitrogen is added. Then,the same amount of the mixture as before is released and replaced by nitrogen for the second time. As a result,the oxygen content becomes $9 \%$ of the total volume. Find the amount of mixture released each time (in litres).

$A$ dishonest milkman professes to sell his milk at cost price but he mixes it with water and thereby gains $25 \%$. The percentage of water in the mixture is?