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?

The ratio of the radii of two cylinders is $2:3$,and the ratio of their heights is $5:3$. The ratio of their volumes will be

The incomes of Gupta and Verma are in the ratio $9: 4$ and their expenditures are in the ratio $7: 3$. If each saves ₹ $2000$,then Gupta's expenditure is (in ₹):

Arti has coins of the denomination of $Rs. 1$,$50 \text{ paise}$,and $25 \text{ paise}$ in the ratio of $12: 10: 7$. The total worth of the coins she has is $Rs. 75$. Find the number of $25 \text{ paise}$ coins.

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 numbers are in the ratio $3: 5$. If $9$ is subtracted from each,the new numbers are in the ratio $12: 23$. The smaller number is: