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?

Answer 1

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

Now, by first condition

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

i.e., x - = 3(y - 2)

so, 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 + 16

x – 2y = 10 …(ii)

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

x – 2y = 10

- (x–3y =- 4)

We get, y = 14

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

x - 2(14) = 10

so, x = 38

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