If $50$ fewer candidates had applied and $25$ fewer had been selected,the ratio of selected to unselected candidates would have been $9:4$. How many candidates had applied if the initial ratio of selected to unselected candidates was $2:1$?

There is $1000 \, \text{litres}$ of milk in a pot. $100 \, \text{litres}$ of milk is taken out and the same amount of water is poured into it. Again, $200 \, \text{litres}$ of the mixture is taken out and the same amount of water is poured into it, and finally, $400 \, \text{litres}$ of the mixture is taken out and the same amount of water is poured into it. What is the amount of milk in the resulting mixture?

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

If $2: x :: 5: 7$,then $x$ is equal to

$A$ and $B$ earn in the ratio $2:1$. They spend in the ratio $5:3$ and save in the ratio $4:1$. If the total monthly savings of both $A$ and $B$ are ₹ $5,000$,the monthly income of $B$ is (in ₹): (in $,000$)

The ratio of the present ages of $R$ and $S$ is $11:17$. $11$ years ago,the ratio of their ages was $11:20$. What is $R$'s present age (in years)?