Question

10.5 years ago the age of a mother was 4 times the age of her daughter. Today
the age of the mother is three times the age of the daughter. Find their
present ages.

Answer 1

Required Answer :

Present age of daughter = 15 years

Present age of mother = 45 years

Given :

• 5 years ago the age of a mother was 4 times the age of her daughter.

• Today the age of the mother is three times the age of the daughter.

To find :

• The present age of mother and her daughter

Solution :

Let,

⇒ The present age of daughter = x years

⇒ The present age of mother = 3(Age of daughter)

⇒ The present age of mother = 3x years

Their ages before 5 years :

⇒ Mother's age = 3x - 5 years

⇒ Daughter's age = x - 5 years

According to the question,

= Mother's age = 4(Daughter's age)

= 3x - 5 = 4(x - 5)

= 3x - 5 = 4x - 20

= 3x - 4x = - 20 + 5

= - x = - 15

= x = 15

Substituting the value of 'x' in the assumed age of daughter and mother :

= Present age of daughter = x

= Present age of daughter = 15 years

= Present age of mother = 3x

= Present age of mother = 3(15)

= Present age of mother = 45 years