4. The sum of the ages of a woman and her daughter is 46 years. In 4 years', time, the ratio of their ages will be 7:2. Find their
present age.

Present age of woman = 38 years.

Present age of Daughter = 8 years.

Explanation:

Given :

The sum of the ages of a woman and her daughter = 46 years.

In 4 years time,the ratio of their ages = 7:2.

Solution :

Let assume,

Present age of woman = x years

Present age of Daughter = y years

as given,

The sum of the ages of a woman and her daughter = 46 years.

x+y = 46

x =   46 - y(equation 1)

and,

In 4 years time, the ratio of their ages =  7:2.

After 4 years,

Age of woman = (x+4) years

Age of daughter = (y+4) years

→ (x+4) : (y +4) = 7:2

→ x+4/y+4 = 7/2

→ 46-y+4/y+4 = 7/2

→ 50-y/y+4 = 7/2

→7y +28 = 100-2y

→ 7y +2y = 100 -28

→ 9y = 72

→ y = 8

so, y = Present age of Daughter = 8 years.

Put the value of y = 8 in equation (1) .

→ x = 46 - y

→ x = 46 - 8

→ x = 38

Thus, the Present age of woman = x = 38 years.