In what ratio must a grocer mix two varieties of tea worth ₹ $60$ a $kg$ and ₹ $65$ a $kg$ so that by selling the mixture at ₹ $68.20$ a $kg$ he may gain $10 \%$?

$4 \, kg$ 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 $kg$).

In three vessels,the ratio of water and milk is $6:7$,$5:9$,and $8:7$,respectively. If the mixtures of the three vessels are combined,what will be the final ratio of water to milk?

$A$ merchant mixes three varieties of rice costing $Rs. 20$ per $kg$,$Rs. 24$ per $kg$,and $Rs. 30$ per $kg$ and sells the mixture at a profit of $20\%$ at $Rs. 30$ per $kg$. How many $kgs$ of the second variety will be in the mixture if $2$ $kgs$ of the third variety is there in the mixture?

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 $kg$?

The cost of Type $1$ rice is $Rs. 15$ per $kg$ and Type $2$ rice is $Rs. 20$ per $kg$. If both Type $1$ and Type $2$ are mixed in the ratio of $2:3$,then the price per $kg$ of the mixed variety of rice is? (in $Rs.$)