Finding the overall profit or loss percentage in a transaction

Let the present age of the father be F and the son be S. The age difference between them is a constant value d = F - S. The statement "n years back I was as old as you are now" means F - n = S \implies n = F - S = d. Thus, the value n is exactly their constant age difference d .

Now look at the second condition: "My present age (F) is four times your age n years back (S - n)" . F = 4(S - d) Substitute S = F - d into the equation: F = 4((F - d) - d) \implies F = 4(F - 2d) \implies F = 4F - 8d \implies 3F = 8d.

We are given the sum of their present ages is 130: F + S = 130 \implies F + (F - d) = 130 \implies 2F - d = 130 \implies d = 2F - 130.

Substitute this expression for d into 3F = 8d: 3F = 8(2F - 130) \implies 3F = 16F - 1040 \implies 13F = 1040 \implies F = 80.

Find d: 3(80) = 8d \implies 240 = 8d \implies d = 30 years.

Answer: (a).