Age from the fractions of a life

An elderly man reviews his life: a quarter of it was boyhood, a fifth was youth, a third was manhood, and the last $13$ years have been old age. What is his age?

60. The three stages make $\tfrac14+\tfrac15+\tfrac13=\tfrac{47}{60}$ of his life, so the $13$ years of old age are the remaining $\tfrac{13}{60}$. Hence he is $60$ (boy $15$, youth $12$, man $20$, old age $13$).