Question

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

• A. Salims age $=68$ years, Daughters age $=24$ years.
• B. Salims age $=58$ years, Daughters age $=74$ years.
• C. Salims age $=23$ years, Daughters age $=14$ years.
• D. Salims age $=38$ years, Daughters age $=14$ years.

Answer 1

The correct option is D Salims age $=38$ years, Daughters age $=14$ years.

Let the age of Salim $=x$ and the age of the daughter $=y$, both in year.

Then two years back their ages are

$x-2$ and $y-2$ respectively.

$\therefore$ by the given condition

$x-2=3(y-2)$

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

Again six years later their ages will be

$x+6$ and $y+6$ respectively.

$\therefore$ by the given condition

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

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

Subtracting (ii) from (i), we get

$-y=-14$

$\Rightarrow y=14$

Putting $y=14$ in (i), we get

$x-3\times 14=-4$

$\Rightarrow x=38$

So, Salim's present age $=38$ yrs and his daughter's present age $=14$ yrs.