Define variables for the current ages.

Step 1: Define variables for the current ages. Let the current age of the father be $F$ years. Let the current age of the son be $S$ years.

Step 2: Formulate equations based on the given conditions. According to the first condition, 10 years ago, the father's age was three times the son's age. Father's age 10 years ago: $F - 10$ Son's age 10 years ago: $S - 10$ So, we have the equation: $F - 10 = 3(S - 10)$ $F - 10 = 3S - 30$ $F = 3S - 20 \quad (*)$

According to the second condition, 10 years from now, the father's age will be twice the son's age. Father's age 10 years from now: $F + 10$ Son's age 10 years from now: $S + 10$ So, we have the equation: $F + 10 = 2(S + 10)$ $F + 10 = 2S + 20$ $F = 2S + 10 \quad (**)$

Step 3: Solve the system of equations to find the current ages. We have two expressions for $F$. Equate them: $3S - 20 = 2S + 10$ Subtract $2S$ from both sides: $3S - 2S - 20 = 10$ $S - 20 = 10$ Add 20 to both sides: $S = 10 + 20$ $S = 30$ The current age of the son is 30 years.

Now substitute $S = 30$ into equation $(**)$ to find $F$: $F = 2(30) + 10$ $F = 60 + 10$ $F = 70$ The current age of the father is 70 years.

Step 4: Calculate the ratio of their current ages. The ratio of the father's current age to the son's current age is $\frac{F}{S}$. $\frac{F}{S} = \frac{70}{30}$ $\frac{F}{S} = \frac{7}{3}$ The ratio of their current ages is $7:3$.

The ratio of their current ages is $\boxed{7:3}$. Send me the next one 📸