Two numbers are in the ratio $1: 2$. If $7$ is added to both,their ratio changes to $3: 5$. The greatest number is

Find two numbers such that their mean proportion is $10$ and their third proportion is $1024$.

$P$ varies inversely with the product of $Q$ and $R$. When $Q = 6$ and $R = 12$,$P = 75$. When $Q = 5$ and $R = 10$,what is the value of $P$?

Out of the number of qualified candidates from State $P$ in $2008,$ the respective ratio of male and female candidates is $11: 7.$ If the number of female qualified candidates from State $P$ in $2008$ is $126,$ what is the total number of qualified candidates (both male and female) from State $P$ in $2008?$

The present ages of Reena and Usha are $24$ and $36$ years,respectively. What was the ratio between the ages of Usha and Reena $8$ years ago?

₹ $1980$ is divided among $A, B$ and $C$ such that half of $A$'s part,one-third of $B$'s part,and one-sixth of $C$'s part are equal. Then $B$'s part is (in ₹):