Divide ₹ $1,000$ among $P, Q,$ and $R$ such that $P$ gets $\frac{2}{3}$ of $Q$'s share and $R$ gets $\frac{5}{3}$ of $Q$'s share. What is the share of $Q$?

$A$ sum of ₹ $15525$ is divided among Sunil,Anil and Jamil such that if ₹ $22$,₹ $35$ and ₹ $48$ be diminished from their shares respectively,their remaining sums shall be in the ratio $7: 10: 13$. What would have been the ratio of their sums if ₹ $16$,₹ $77$ and ₹ $37$ respectively were added to their original shares?

$A$ certain sum of money was divided between $A$,$B$,and $C$ in the ratio $5: 6: 9$. If $A$ received ₹ $450$,what was the total sum divided?

Calculate the fourth proportional to the numbers $286, 78, 1342$.

The ratio of two numbers is $3:4$ and their sum is $420$. The greater of the two numbers is

$A$ sum of ₹ $1,300$ is divided amongst $P, Q, R$ and $S$ such that $\frac{P \text{'s share}}{Q \text{'s share}} = \frac{Q \text{'s share}}{R \text{'s share}} = \frac{R \text{'s share}}{S \text{'s share}} = \frac{2}{3}$. Then $P$'s share is (in ₹):