The ratio of a father’s age to his son’s age is 4 : 1. The product of their ages is 196. What will be the ratio of their ages after 5 years?

Step 1: Let's denote the father's age as 4x and the son's age as x. The problem states that the product of their ages is 196. So we can set up the equation 4x * x = 196.

Step 2: Simplify the equation to 4x^2 = 196.

Step 3: Solve for x^2 by dividing both sides of the equation by 4. This gives us x^2 = 49.

Step 4: Take the square root of both sides to solve for x. This gives us x = 7.

Step 5: Now that we know x = 7, we can find the father's age by multiplying 4x, which gives us 4*7 = 28. So, the father is 28 years old and the son is 7 years old.

Step 6: The problem asks for the ratio of their ages in 5 years. In 5 years, the father will be 33 years old and the son will be 12 years old.

Step 7: The ratio of their ages in 5 years will be 33 : 12.

Let's solve this step by step:

Step 1: Let's assume the father's age is 4x and the son's age is x. The product of their ages is 196. So, we can write the equation as 4x * x = 196.

Step 2: Simplifying the equation gives us 4x^2 = 196.

Step 3: Solving for x^2, we get x^2 = 196/4 = 49.

Step 4: Taking the square root of both sides, we get x = 7.

Step 5: So, the father's age is 4x = 4*7 = 28 years and the son's age is x = 7 years.

Step 6: After 5 years, the father's age will be 28 + 5 = 33 years and the son's age will be 7 + 5 = 12 years.

Step 7: Therefore, the ratio of their ages after 5 years will be 33 : 12.