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Arun's present age is one third of the age of his father. After 15 years, his age will be one half of age of his father. How old is Arun's father at present ?

  • A.30
  • B.15
  • C.60
  • D.45

Answer: D

Arun's father is 45 years old.

Let the father's present age be \(F\), so Arun is \(F/3\). In 15 years Arun will be half his father's age:

\[ \begin{aligned} \tfrac{F}{3} + 15 &= \tfrac{1}{2}(F + 15) \\ 2F + 90 &= 3F + 45 \\ F &= 45 \end{aligned} \]

Check: Arun is 15 now; in 15 years he will be 30 and his father 60, exactly half. The option 15 is Arun's age, not his father's.

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