Answer:
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.
