Question

The sum of the ages of a daughter and her mother is 56 years. After four years, the age of the mother will be three times that of the daughter. Find their present ages.
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Answer 1

Answer

Present age of daughter = 12 years

Present age of mother = 44 years

Given

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

To Find

Present ages

Solution

Let the present age of daughter be , " x "

Present age of mother be , " y "

A/c , " The sum of the ages of a daughter and her mother is 56 years "

⇒ x + y = 56 ... (1)

A/c , " After four years, the age of the mother will be three times that of the daughter "

⇒ ( y + 4 ) = 3 ( x + 4 )

⇒ y + 4 = 3x + 12

⇒ y - 3x = 8 ... (2)

Solve (1) - (2) ,

⇒ ( x + y ) - ( y - 3x ) = 56 - 8

⇒ x + y - y + 3x = 48

⇒ 4x = 48

⇒ x = 12

On sub. x value in (1) , we get ,

⇒ y = 56 - $\rm 12$

⇒ y = 44

So , Present age of daughter , x = 12 years

Present age of mother , y = 44 years

Answer 2

EXPLANATION.

• GIVEN

Sum of the age of a daughter and her

mother is = 56 years.

After 4 years,the age of the mother will be

three times that of the daughter.

Find their present age.

According to the question,

Let the present daughter age = x years

Let the mother present age = y years.

=> x + y = 56 ......(1)

After 4 years,

Daughter age = x + 4

mother age = y + 4

According to the question,

mother will be three times that of daughter.

=> y + 4 = 3 ( x + 4 )

=> y + 4 = 3x + 12

=> y - 3x = 8 ......(2)

From equation (1) and (2) we get,

=> 4x = 48

=> x = 12

put the value of x = 12 in equation (1)

we get,

=> 12 + y = 56

=> y = 44

Therefore,

present age of daughter = 12 years.

present age of mother = 44 years.