A person's present age is two-fifths of his mother's age. After 8 years, he will be half of his mother's age. How old is the mother now?

Problem restatement
Relate present ages using a ratio; after 8 years the ratio becomes 1:2. Solve the two linear relations to find the mother's current age.

Given data

• Let person's age = P, mother's age = M.
• P = (2/5)M.
• P + 8 = (1/2)(M + 8).

Concept/Approach
Substitute the ratio into the future-age relation to eliminate one variable and solve.

Step-by-Step calculation
(2/5)M + 8 = (1/2)(M + 8)Multiply by 10: 4M + 80 = 5M + 4080 − 40 = 5M − 4M ⇒ M = 40

Verification/Alternative
Then P = (2/5)×40 = 16. After 8 years: P = 24, M = 48 → P is half of M (24 = 48/2), as required.

Common pitfalls
Confusing “two-fifths of mother” with “mother is two-fifths of person.” The ratio is P:M = 2:5.

Final Answer
40 years