In ten years time a father will be twice as old as his son. 10 years ago he was six times as old as his son how old are day now?

Let's assume the current age of the son is S and the current age of the father is F.

According to the given information, in ten years, the father will be twice as old as his son. So, we can write the equation:

F + 10 = 2(S + 10)

Expanding the equation, we get:

F + 10 = 2S + 20

Now, let's consider the second piece of information. Ten years ago, the father was six times as old as his son. So, we can write the equation:

F - 10 = 6(S - 10)

Expanding the equation, we get:

F - 10 = 6S - 60

Now, we have a system of two equations:

F + 10 = 2S + 20 ...(1)
F - 10 = 6S - 60 ...(2)

Solving this system of equations will give us the current ages of the son (S) and the father (F).

From equation (1), we can rewrite it as:

F = 2S + 10 ...(3)

Substituting equation (3) into equation (2), we get:

2S + 10 - 10 = 6S - 60

2S = 6S - 60

4S = 60

S = 15

Substituting the value of S back into equation (3), we get:

F = 2(15) + 10

F = 30 + 10

F = 40

Therefore, the current age of the son is 15 years old, and the current age of the father is 40 years old.

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