A's present age is two-fifths of the age of his mother. After 8 years, his age will be half of the age of his mother. How old is the mother at present?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 40 years
A’s age is two-fifths of his mother’s, so the two present ages can be written as 2 parts and 5 parts of the same size. In 8 years both ages grow by 8, and then A’s age is half his mother’s.
Present ages: A \(=2x\), mother \(=5x\)
After 8 years: \(\displaystyle 2x+8=\frac{1}{2}(5x+8)\)
\(4x+16=5x+8\), so \(x=8\)
Mother’s present age \(=5\times8=40\) years (A is 16)