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 $kg$?

In what ratio should wheat at ₹ $32$ per $kg$ be mixed with wheat at ₹ $24$ per $kg$ so that on selling the mixture at ₹ $39$ per $kg$,there is a profit of $30 \%$?

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

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?

$A$ bottle full of whisky contains $50 \%$ alcohol. $A$ part of this whisky is replaced by another containing $18 \%$ alcohol and the percentage of alcohol was found to be $26 \%$. The quantity of whisky replaced is

How many kg of sugar costing ₹ $11.70/kg$ must be mixed with $24$ $kg$ of sugar costing ₹ $8.1/kg$ so that there may be a gain of $15 \%$ by selling the mixture at ₹ $9/kg$? (in $kg$)