Question

The present age of a woman is 3 years more than three times the age of her daughter.Three years hence , the woman's age will be 10 years more than twice the age of he daughter.Find their present ages.

Answer 1

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Answer 2

Answer:

Step-by-step explanation:

Given :-

The present age of a woman is 3 years more than three times the age of her daughter.

Three years hence , the woman's age will be 10 years more than twice the age of he daughter.

To Find :-

Their present ages.

Solution :-

Let the woman’s present age be x years.  

Let her daughter’s present age be y years.  

According to the Question

1st Equation

⇒ x = 3y + 3  

⇒ x – 3y = 3 …….(i)

2nd Equation

After three years, we have:  

⇒ (x + 3) = 2(y + 3) + 10  

⇒ x + 3 = 2y + 6 + 10  

⇒ x – 2y = 13 ……(ii)  

Subtracting (ii) from (i)

⇒ -y = (3 – 13)

⇒ y = 10  

Putting y value in Eq (i)

⇒ x – 3y = 3

⇒ x – 3 × 10 = 3  

⇒ x – 30 = 3  

⇒ x = (3 + 30)

⇒ x = 33  

Hence, the woman’s present age is 33 years and her daughter’s present age is 10 years.