In a mixture of milk and water with a total volume of $60$ $L$,the ratio of milk to water is $7:5$. How much water must be added to make the ratio of milk to water equal $(1:1)$? (in $L$)

The ratio of alcohol and water in $40$ $litres$ of mixture is $5:3$. Then $8$ $litres$ of the mixture is removed and replaced with water. Now,the ratio of the alcohol and water in the resultant mixture is

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 $kg$?

Pencils at $Rs. 4.20$ per dozen are mixed with pencils at $Rs. 5.40$ per dozen in the ratio $3:5$. Find the price per dozen of the mixture (in $Rs.$).

The cost of Type $1$ rice is ₹ $15/kg$ and Type $2$ rice is ₹ $20/kg$. 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 ₹):

Two types of alloys contain gold and silver in the ratio of $7: 22$ and $21: 37.$ In what ratio should these alloys be mixed,so as to have a new alloy in which gold and silver would exist in the ratio $25: 62?$