Question

Father's age is five times the age of his daughter. After 6 more year's father's age will
be three times her age. Find father's present age.
​

Answer 1

Step-by-step explanation:

Let the father's present age be x and daughter's present age be y respectively,

Therefore, according to the question,

x = 4y -equation-(1)

After 6 years,

father's age = x + 6

and daughter's age = y + 6

Now, according to the question,

(x + 6) = 3(y + 6) -equation-(2)

On simplifying equation-(2) , we get,

(x + 6) = 3y + 18

》x + 6 = 18 + 3y

》 x = 18 - 6 + 3y

》 x = 12 + 3y -equation-(3)

From equation-(1) and equation-(3) , we have,

4y = 12 + 3y

》4y - 3y = 12

》y = 12 -equation-(4)

Hence, daughter's present age is 12 years.

Now, from equation-(1) and equation-(4) ,

x = 4 × 12

》x = 48

Hence, father's present age is 48 years.

Now, observing the father's and the daughter's present ages that are 48 and 12 years respectively, it is clearly evident that the father is ‘four times’ the age of his daughter (i.e. 48 = 4 × 12) .

Therefore, after 6 years,

father's age = 48 + 6 = 54

and

daughter's age = 12 + 6 = 18

Now, observing the father's and the daughter's age after 6 years that are 54 and 18 years respectively, it is clearly evident that the father is ‘three times’ the age of his daughter (i.e. 54 = 3 × 18).

Therefore at last, ‘further’ after 6 years,

father's age = 54 + 6 = 60

and

daughter's age = 18 + 6 = 24

Now at last, observing the father's and the daughter's age after 6 years further 6 years from the present, that is after 12 years that are 60 and 24 years respectively, it is clearly evident that the father is ‘five times’ the age of his daughter (i.e. 60 = 5 × 12).

Therefore, we can conclude that 6 years further after 6 years from the present, that is a total of after 12 years, the father would be “five times” the age of his daughter.