Gold is $19$ times as heavy as water and copper is $9$ times as heavy as water. In what ratio should these be mixed to get an alloy $15$ times as heavy as water?

An alloy of copper and zinc is taken in the ratio $1: 2$,and another alloy of the same metals is taken in the ratio of $2: 3$. How many parts of the two alloys must be taken to obtain a new alloy consisting of copper and zinc that are in the ratio $3: 5$?

If $A: B = 8: 15$,$B: C = 5: 8$,and $C: D = 4: 5$,then $A: D$ is equal to:

If $x$ runs are scored by $A$,$y$ runs by $B$,and $z$ runs by $C$,then $x: y = y: z = 3: 2$. If the total number of runs scored by $A$,$B$,and $C$ is $342$,the runs scored by each would be respectively:

The ratio of the incomes of $A$ and $B$ is $5:4$ and the ratio of their expenditures is $3:2$. If at the end of the year,each saves $Rs. 1600$,then the income of $A$ is (in $Rs.$):

Find the third proportional to the numbers $4$ and $42$.