The problem you're asking is:

1. The ratio of the ages of the mother and daughter is 2:1.
2. Four years ago, the ratio of the son's age to the daughter's age was 3:4.
3. The father is 5 years older than the mother.
4. Two years ago, the father's age was 3 times the son's age.

You are asked to find the daughter's current age.

Let’s denote:

• The daughter's current age as $x$.
• The mother's current age as $2x$ (from the given ratio 2:1).

Step 1: Relationship of ages 4 years ago

• The son's age 4 years ago: $S - 4$.
• The daughter's age 4 years ago: $x - 4$.
• According to the problem, $\frac{S - 4}{x - 4} = \frac{3}{4}$, where $S$ is the son's current age.

We can express the son's age in terms of the daughter's age by solving this equation.

Step 2: Father's age

• The father's current age is $2x + 5$, since the father is 5 years older than the mother.
• Two years ago, the father's age was $2x + 5 - 2 = 2x + 3$.
• Two years ago, the son's age was $S - 2$, and the problem states that the father's age then was 3 times the son's age: $2x + 3 = 3(S - 2)$

Now, we have two equations:

1. $\frac{S - 4}{x - 4} = \frac{3}{4}$
2. $2x + 3 = 3(S - 2)$

Let’s solve this system of equations to find the daughter’s age.

I'll solve these now.The solution indicates that the daughter's current age is 24 years, and the son's current age is 19 years.

Thus, the answer to the question is:

E. 24 years

Do you have any questions or would you like a detailed explanation of the steps?

Related questions:

1. How do we derive the equation for the son and daughter's age ratio 4 years ago?
2. How does the father’s age equation affect the solution?
3. What would the mother’s and father’s current ages be?
4. How can we verify the correctness of the solution?
5. How would the problem change if the age ratios were different?

Tip:

Always set up equations clearly for each condition in the problem before solving the system; it helps avoid confusion in complex word problems.