Tanay divided the collection of $253$ stamps between his two sisters Shamali and Keya in a ratio of $6:5$. Find the number of stamps each of the sisters received.

Divide a line segment $45 cm$ into three parts whose ratio is $5:7:3$.

Two numbers are in a ratio of $3:7$. If $4$ is added to each of them, then the ratio becomes $1:2$. Find the numbers.

Two numbers are in a ratio of $4:5$.If $7$ is subtracted from each of them, then the ratio becomes $3:4$. Find the numbers.

What number must be added to each term of the ratio $7:5$, so that the ratio becomes $5:4$?

What number must be subtracted from each term of the ratio $15:23$, so that the ratio becomes $7:15$?

The ages of $A \& B$ are in a ratio of $3:5$. Eight years hence, their ages will be in a ratio of $5:7$. Find their present ages.

If $x:y=3:5$, find $(2x+3y):\left(5x+7y\right)$

If $\left(3a+2b\right):\left(2a+5b\right)=12:19$, find $a:b$.