$4 \, kg$ of potato at $Rs. \,5$ per $kg$ is mixed with $8 \,kg$ of potato at $Rs. \,6$ per $kg.$ Find the average price of the mixture (in $Rs.$ per $kg$).

Zinc and copper are in the ratio $5:3$ in $400 \, g$ of an alloy. How much copper (in $g$) should be added to make the ratio $5:4$?

Two casks of $48$ $litres$ and $42$ $litres$ are filled with mixtures of wine and water,the proportions in the two casks being respectively $13:7$ and $18:17$. If the contents of the two casks are mixed,and $20$ $litres$ of water is added to the whole,what will be the proportion of wine to water in the resultant mixture?

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 varieties of sugar are mixed together in a certain ratio. The cost of the mixture per $kg$ is ₹ $0.50$ less than that of the superior and ₹ $0.75$ more than the inferior variety. The ratio in which the superior and inferior varieties of sugar have been mixed is

In a mixture of milk and water of volume $30$ $L$,the ratio of milk and water is $8:7$. How much water should be added to the mixture to make the ratio $4:5$? (in $L$)