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?

Answer 1

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

Now, by first condition,

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

i.e., x – 2 = 3(y – 2)

⇒ x – 2 = 3y – 6

⇒ x – 3y = – 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

⇒ x + 6 = 2y + 12 + 4

⇒ x – 2y = 16 – 6

⇒ x – 2y = 10  ......(ii)

On subtracting equation (i) from equation (ii), we get

x – 2y = 10
x – 3y = – 4
–    +        + 
       y = 14

Put the value of y in equation (ii), we get

x – 2 × 14 = 10

⇒ x = 10 + 28

⇒ x = 38

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