$A$ and $B$ are two alloys of gold and copper prepared by mixing metals in the ratio $7:2$ and $7:11$ respectively. If equal quantities of the alloys are melted to form a third alloy $C$,the ratio of gold and copper in $C$ will be

What is the fourth proportional to $189, 273$ and $153$?

If $a:b = \frac{2}{9} : \frac{1}{3}$,$b:c = \frac{2}{7} : \frac{5}{14}$,and $d:c = \frac{7}{10} : \frac{3}{5}$,then find $a:b:c:d$.

Two candles of the same height are lighted at the same time. The first is consumed in $8 \text{ hours}$ and the second in $6 \text{ hours}$. Assuming that each candle burns at a constant rate,in how many hours after being lighted,the ratio between the height of the first and second candles becomes $2:1$?

If $(x+y):(x-y)=11:1$,find the value of $\frac{(5x+3y)}{(x-2y)}$.

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?