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 ₹ $16.5/kg$?

Two vessels contain milk and water in the ratio $3:2$ and $7:3$. Find the ratio in which the contents of the two vessels have to be mixed to get a new mixture in which the ratio of milk and water is $2:1$.

$300$ $gm$ of sugar solution contains $40 \%$ sugar. How much sugar (in $gm$) should be added to make the concentration $50 \%$ in the solution?

$A$ shopkeeper bought $30 \text{ kg}$ of rice at the rate of $₹ 70$ per $\text{kg}$ and $20 \text{ kg}$ of rice at the rate of $₹ 70.75$ per $\text{kg}$. If he mixed the two brands of rice and sold the mixture at $₹ 80.50$ per $\text{kg}$,his total gain is (in $₹$):

Solution $A$ contains $10 \%$ acid and solution $B$ contains $30 \%$ acid. In what ratio should solution $A$ be mixed with solution $B$ to obtain a mixture with $25 \%$ acid?

$A$ man buys $2$ cows for $Rs. 2700$ and sells one at a loss of $6\%$ and the other at a gain of $7.5\%$. On the whole,he neither gained nor lost. What is the cost price of the $2^{nd}$ cow?