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 ages.
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Answer:
the age of a woman is 29yrs and the age of daughter is 8yrs.
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GIVEN :
- 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.
To find :
- The present ages = ?
STEP BY STEP EXPLAINATION :
=> Present age of woman = x years
=> Present age of Daughter = y years
According to the 1st condition :-
The sum of the ages of a woman and her daughter is 46 years.
{x+y=46}→x+y=46
{x=46-y.................(1)}→x=46−y.................(1)
According to the 2nd condition :-
In 4 years time,the ratio of their ages will be 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
Present age of Daughter = 8 years.
Now put y = 8 in eq(1) .
→ x = 46 - y
→ x = 46 - 8
→ x = 38
Therefore, The Present age of woman = 38 years.
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