Question

the daughter age is 5 years and mother age is 32 years old after x years the mothers age will be four times of her daughter what is the value of x?
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Answer 1

Mother’s current age = 45 years

In 5 years, mother’s age = 5 x daughter’s age. => Mother’s future age is divisible by 5.

The time difference between now and future time is also divisible by 5. So, mother’s current age is divisible by 5 by the following relation:

5 n = 5 m - 5 p ; n,m,p are Integers (belong to Z)

Youngest mother’s current age = 9 x 5 = 45. So, daughter’s current age = 5.

Let’s test our hypothesis now:

m = 9 x d …(1) for present time

m + 5 = 5 ( d + 5) …(2) for future time

9 x d + 5 = 5 x d + 25 [using (1) in (2)]

4 x d = 20

Daughter’s present age, d = 5 years.

So, mother’s present age = 9 x 5 = 45 years.