**Question:**

Two years ago, Salim was thrice as old as his daughter and six years later, he will be four year older than twice her age. How old are they now?

**Solution:**

Let Salim and his daughter’s age be x and y yr respectively.

Now, by first condition

Two years ago, Salim was thrice as old as his daughter.

i.e. $\quad x-2=3(y-2) \Rightarrow x-2=3 y-6$

$\Rightarrow \quad x-3 y=-4$ ....(i)

and by second condition, six years later. Salim will be four years older than twice her age.

$x+6=2(y+6)+4$

$\Rightarrow \quad x+6=2 y+12+4$

$\Rightarrow \quad x-2 y=16-6$

$\Rightarrow \quad x-2 y=10$ ......(ii)

On subtractina Eq. (i) from Eq. (ii), we get

Put the value of $y$ in Eq. (ii), we get

$x-2 \times 14=10$

$\Rightarrow \quad x=10+28 \Rightarrow x=38$

Hence, Salim and his daughter’s age are 38 yr and 14 yr, respectively.