Question

The sum of the present ages of Rani and her father is 43 years. Six years hence, father will be 4 times as old as his daughter. Find their present ages.

Answer 1

Here, let Rani’s present age be x and her father’s be y.

Given:

x + y = 43    ...(1)

According to the given condition (Six years hence):

y + 6 = 4(x + 6)

y = 4x + 18    ...(2)

Now, substituting equation (2) into (1):

x + (4x + 18) = 43

5x + 18 = 43

5x = 43 − 18

5x = 25

x = `25/5`

∴ x = 5

Let’s substitute x = 5 in equation (1)

x + y = 43

y = 43 − x

y = 43 − 5

∴ y = 38

Hence, the present ages of Rani and his father are 5 years and 38 years, respectively.