Question

Question 16
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?

Answer 1

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
$i.e.,x-2=3(y-2)\Rightarrow x-2=3y-6\Rightarrow x-3y=-4$
and by second condition, six years later. Salim will be four years older than twice her age.
x + 6 = 2 (y + 6 ) + 4
$\Rightarrow$ x + 6 = 2y + 12 + 4
$\Rightarrow$ x – 2y = 16 – 6
$\Rightarrow$ x – 2y = 10
On subtracting Eq. (i) from Eq. (ii), we get
$x-2y=10x-3y=-4\underset{–}{}y=14$
put the value of in Eq. (ii) we get
x – 2y × 14 = 10
x = 10 + 28 $\Rightarrow$ x = 38
hence, salim and his daughter’s age are 38 yr and 14 yr respectively.