A person’s present age two-fifth of the age of his mother. After 8 yr, he will be one-half of the age of the age of his mother. What is the present age of the mother?
Explanation
1. Define the Variables:
Let the present age of the Mother be x.
According to the question, the Person's present age is 25 of the mother's age.
Person's present age=2x5
2. Set up the Equation (After 8 years):
After 8 years, both their ages will increase by 8.
Mother's age =x+8
Person's age =2x5+8
The problem states that at this time, the person will be one-half (12) of his mother's age:
2x5+8=12(x+8)
3. Solve for x:
Multiply the entire equation by 10 (the LCM of 5 and 2) to remove fractions:
10(2x5+8)=10(x+82)
2(2x)+80=5(x+8)
4x+80=5x+40
Rearrange the terms to solve for x:
80−40=5x−4x
x=40
4. Final Answer:
The mother's present age is 40 years.
Correct Option: (A) 40 yr
Explanation
1. Define the Variables:
Let the present age of the Mother be x.
According to the question, the Person's present age is 25 of the mother's age.
Person's present age=2x5
2. Set up the Equation (After 8 years):
After 8 years, both their ages will increase by 8.
Mother's age =x+8
Person's age =2x5+8
The problem states that at this time, the person will be one-half (12) of his mother's age:
2x5+8=12(x+8)
3. Solve for x:
Multiply the entire equation by 10 (the LCM of 5 and 2) to remove fractions:
10(2x5+8)=10(x+82)
2(2x)+80=5(x+8)
4x+80=5x+40
Rearrange the terms to solve for x:
80−40=5x−4x
x=40
4. Final Answer:
The mother's present age is 40 years.
Correct Option: (A) 40 yr
