Step-by-step Solution:

Quick Solution

The best way to solve this age puzzle is by translating the given information into two algebraic equations.

1. Set Up the Equations

- Let the person's present age be P and the mother's present age be M.

- From the first sentence ("A person's present age is two fifth of the age of his mother"):
P = (2/5)M

- In 8 years, their ages will be (P + 8) and (M + 8). From the second sentence ("After 8 years, he will be one-half of the age of his mother"):
P + 8 = (1/2)(M + 8)

2. Solve for the Mother's Age (M)

- Substitute the first equation into the second one to eliminate P and solve for M:
(2/5)M + 8 = (1/2)(M + 8)

- Now, solve the equation:
(2/5)M + 8 = (1/2)M + 4
8 - 4 = (1/2)M - (2/5)M
4 = (5/10 - 4/10)M
4 = (1/10)M
M = 4 × 10 = 40.

3. Verification (Optional)

- If the mother's present age is 40, the person's current age is (2/5) × 40 = 16.
- In 8 years, the mother will be 48 and the person will be 24.
- 24 is exactly half of 48, so the answer is correct.

Final Answer: The present age of the mother is 40 years.