The father is 5 years older than the mother. The difference between total age of father & son and mother & daughter is 15 years . Also the total age of children is 20 years, then the age of the son is _____

Options

A. 10 years
B. 15 years
C. 20 years
D. 25 years

Answer

To solve the problem step by step, we will define the variables and set up the equations based on the information given in the question.

### Step 1: Define Variables
Let:
- The age of the mother be \( x \).
- The age of the father, who is 5 years older than the mother, be \( x + 5 \).
- The age of the son be \( y \).
- The age of the daughter be \( z \).

### Step 2: Set Up the Equations
From the problem, we have two key pieces of information:

1. The difference between the total age of the father and son and the total age of the mother and daughter is 15 years. This can be expressed as:
\[ (x + 5 + y) - (x + z) = 15 \]
Simplifying this gives:
\[ y - z + 5 = 15 \]
Therefore, we can rearrange it to form our first equation:
\[ y - z = 10 \quad \text{(Equation 1)} \]

2. The total age of the children (son and daughter) is 20 years:
\[ y + z = 20 \quad \text{(Equation 2)} \]

### Step 3: Solve the Equations
Now we have two equations:
1. \( y - z = 10 \)
2. \( y + z = 20 \)

We can solve these equations simultaneously.

#### Adding the two equations:
\[ (y - z) + (y + z) = 10 + 20 \]
This simplifies to:
\[ 2y = 30 \]
Thus, we find:
\[ y = 15 \]

#### Now, substituting \( y = 15 \) back into Equation 2 to find \( z \):
\[ 15 + z = 20 \]
This gives:
\[ z = 20 - 15 = 5 \]

### Conclusion
The age of the son \( y \) is **15 years**.