The present ages of A and B are in the ratio$5:3$ , after $6years$  their ages are

in the ratio $7:5$ . The present age of A is ________ years

The present age of $A$  and $B$  are in the ratio$=5:3$

$=5x:3x$

The ratio of ages of $A$  and $B$  after $6-years$ $=7:5$

i.e. $\left(5x+6\right):\left(3x+6\right)=7:5$

$\frac{5x+6}{3x+6}=\frac{7}{5}$

$25x+30=21x+42$

$25x-21x=42-30$

$4x=12$

$x=3$

$\therefore$  The present age of $A=5x$

$=5\left(3\right)$

$=15$ .