Question

The sum of the ages of a daughter and mother is 56 years; after four years the age of the mother will be three times that of the daughter. What is the age of the daughter and the mother, respectively?

12 years, 41 years
12 years, 30 years
11 years, 34 years
12 years, 44 years
21 years, 42 years

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Answer 1

Daughter's age = 12 years

Mother's age = 44 years

Step-by-step explanation:

Given -

• The sum of the ages of a daughter and mother is 56 years.
• After four years the age of the mother will be three times that of the daughter.

To find -

• The age of the daughter and the mother.

Solution -

Let the age of the daughter be 'x' years.

Let the age of the mother will be 'y' years.

Four years later,

Daughter's age = (x + 4) years.

Mother's age = (y + 4) years .

According to the first statement,

x + y = 56

→ y = 56 - x---------- (i)

Now, according to the second statement,

y + 4 = 3(x + 4)

→ y + 4 = 3x + 12

→ y - 3x = 12 - 4

→ y - 3x = 8

→ 56 - x - 3x = 8 [from (i)]

→ - 4x = 8 - 56

→ - 4x = - 48

→ x = -48/ -4

→ x = 12 years. [putting in (i)]

→ y = 56 - 12

→ y = 44 years.

Therefore, daughter's age is 12 years and mother's age is 44 years.

More to know -

• $( + )( + ) = ( + )$
• $( + )( - ) = (- )$
• $( - )( + ) = ( - )$
• $( - )( - ) = ( + )$