In what proportion must pulses of $Rs. 70$ per $kg$ be mixed with pulses of $Rs. 45$ per $kg$ to get a mixture of $Rs. 60$ per $kg$?

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 $2:1$.

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

In what ratio should sugar at ₹ $30$ per $kg$ be mixed with sugar at ₹ $45$ per $kg$ so that on selling the mixture at ₹ $42$ per $kg$ there is a profit of $20 \%$?

In what ratio must water be mixed with milk to gain $16 \frac{2}{3} \%$ on selling the mixture at cost price?

The ratio in which two sugar solutions of the concentrations $15 \%$ and $40 \%$ are to be mixed to get a solution of concentration $30 \%$ is