If $5 \ kg$ of potato costing $Rs. 5$ per $kg$ and $3 \ kg$ of potato costing $Rs. 4$ per $kg$ are mixed,find the average cost of the mixture per $kg$?

$A$ and $B$ are two alloys of gold and copper prepared by mixing metals in the ratio $5:3$ and $5:11,$ respectively. Equal quantities of these alloys are melted to form a third alloy $C.$ The ratio of gold and copper in the alloy $C$ is

$A$ person has a chemical costing $Rs. 25$ per $litre$. In what ratio should water be mixed in the chemical so that by selling the mixture at $Rs. 20$ per $litre$,he may get a profit of $25\%$?

$A$ dishonest milkman professes to sell his milk at cost price but he mixes it with water and thereby gains $25 \%$. The percentage of water in the mixture is: (in $\%$)

$A$ person travels $285 \text{ km}$ in $6 \text{ hours}$ in two stages. In the first part of the journey,he travels by bus at a speed of $40 \text{ km/h}$. In the second part of the journey,he travels by train at a speed of $55 \text{ km/h}$. How much distance did he travel by train? (in $\text{km}$)

$A$ mixture contains $80 \%$ acid and the rest water. What part of the mixture should be removed and replaced by the same amount of water to make the ratio of acid to water $4:3$?