Question

53. Eight year ago, Poorvi's age was equal to the sum of
the present ages of her one son and one daughter.
Five years hence, the respective ratio between the
ages of her daughter and her son that time will be
7:6. If Poorvi's husband is 7 years elder to her and
his present age is three times the prevent age of
their son, what is the present age of the daughter?
(in years)​

Answer 1

Given:

Eight years ago, Poorvi's age was equal to the sum of  the present ages of her one son and one daughter

Five years hence, the respective ratio between the  ages of her daughter and her son that time will be  7:6

If Poorvi's husband is 7 years elder to her and  his present age is three times the prevent the age of  their son

To find:

The present age of the daughter (in years)

Solution:

Let's assume,

5 years hence:

Daughter's age → "7x" years

Son's age → "6x" years  

∴ Daughter's present age will be = (7x - 5) years

and

∴ Son's present age will be = (6x - 5) years

8 years ago:

Poorvi's age was given as = [Present age of son] + [Present age of daughter]

⇒ Poorvi's age = (7x - 5) + (6x - 5) = 13x - 10

∴ After 8 years, Poorvi's present age will be = (13x - 10 + 8) years = (13x - 2) years

Now,

Poorvi's husband's present age is given to be 7 years more than Poorvi's present age

∴ Poorvi's husband's present age is = (13x - 2 + 7) = (13x + 5) years

According to the question,  we have

[Poorvi's husband's present age] = 3 × [Son's present age]

⇒ 13x + 5 = 3 × (6x - 5)

⇒ 13x + 5 = 18x - 15

⇒ 18x - 13x = 15 + 5

⇒ 5x = 20

⇒ x = $\frac{20}{5}$

⇒ x = 4

∴ Their daughter's present age = 7x - 5 = (7×4) − 5 = 28 - 5 = 23 years

Thus, the present age of the daughter is 23 years.

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