The third proportional of $12$ and $18$ is

An amount of money is to be divided among $P$,$Q$,and $R$ in the ratio of $3:5:7$,respectively. If the amount received by $R$ is ₹ $4,000$ more than the amount received by $Q$,what will be the total amount (in ₹) received by $P$ and $Q$ together?

$A$ man spends $Rs. 2310$ on an average during the first $8$ months from his income. During the next $4$ months,he spends $Rs. 1800$ on an average from his income,but he had taken a loan of $Rs. 1680$ apart from his income to meet his expenses. If he spent all that he had,what is the ratio of his average income to his average expenditure?

₹ $600$ is divided among $A, B$ and $C$. If $\frac{2}{5}$ of $A$'s share plus ₹ $40$,$\frac{2}{7}$ of $B$'s share plus ₹ $20$,and $\frac{9}{17}$ of $C$'s share plus ₹ $10$ are all equal,then $A$'s share is (in ₹):

In a mixture of $60 \ L$,the ratio of milk and water is $2:1$. What quantity of water (in $L$) should be added so that the ratio becomes $1:3$?

Two numbers are in the ratio $5:3$. If $9$ is subtracted from each,the new ratio becomes $9:5$. What are the two numbers?