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

What must be added to each term of the ratio $2:5$ so that it may equal to $5:6$?

If $B: A = 2: 3$ and $A: C = 5: 7$,then what is $(A + B) : (B + C)$?

$A$ mixture contains alcohol and water in the ratio of $12: 5$. On adding $14 \text{ litres}$ of water,the ratio of alcohol to water becomes $4: 3$. The quantity of alcohol in the mixture is (in $\text{litres}$):

In two alloys,gold and silver are in the ratios of $4:1$ and $1:3$. After alloying together $10 \text{ kg}$ of the first alloy,$16 \text{ kg}$ of the second,and several kilograms of pure gold,an alloy was obtained in which the ratio of gold to silver was $3:2$. Find the weight of the new alloy (in $\text{kg}$).

$A$ box contains $210$ coins of denominations $Rs. 1$ and $50$ paise. The ratio of their respective values is $13: 11$. The number of $Rs. 1$ coins is: