The ratio of the present ages of a son and his father is $1:3$. Four years from now, the father's age will be $\frac{5}{2}$ times the son's age at that time. What was the father's age four years ago?

Question

Accepted Answer

**Solution:**

1. Let the present age of the son be $x$ years. Then, the present age of the father is $3x$ years (given ratio $1:3$).

2. After 4 years, the son's age will be $x + 4$ and the father's age will be $3x + 4$.

3. According to the problem, at that time, the father's age will be $\frac{5}{2}$ times the son's age:
   
   $$3x + 4 = \frac{5}{2} (x + 4)$$

4. Multiply both sides by 2 to eliminate the fraction:

$$2(3x + 4) = 5(x + 4)$$

$$6x + 8 = 5x + 20$$

5. Rearranging terms:

$$6x - 5x = 20 - 8$$

$$x = 12$$

6. So, the present age of the son is $12$ years, and the father's present age is $3 	imes 12 = 36$ years.

7. The father's age four years ago was:

$$36 - 4 = 32 	ext{ years}$$

**Answer:** $32$ years

Answer

Answer

Answer

Answer