Father says to son "I am $5$ times as old as you were when i was as old as you are". If sum of their ages is $56$, what is the age of the father?

Let the father's present age be F and the son's present age be S, so F + S = 56. The phrase about the father being as old as the son means the age difference F minus S equals the time elapsed, and the son's age at that past time was S minus the difference, which equals 2S minus F. The equation given is F = 5 times the quantity 2S minus F, which expands to F = 10S minus 5F, so 6F = 10S, and this simplifies to the ratio 3S = 5F. Substituting S = 56 minus F into 3S = 5F gives 3 times the quantity 56 minus F equals 5F, which means 168 = 8F. Solving for F gives the father's age as 40.

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