In a family, mother's age is twice that of daughter's age. Father is 10 years older than mother. Brother is 20 years younger than his mother and 5 years older than his sister. What is the age of the father?

Options

A. 62 years
B. 60 years
C. 58 years
D. 55 years

Explanation

To solve the problem step by step, we will define the ages of the family members using variables and then set up equations based on the information given in the question.

### Step 1: Define Variables
Let:
- \( D \) = Daughter's age
- \( M \) = Mother's age
- \( F \) = Father's age
- \( B \) = Brother's age

### Step 2: Set Up Equations Based on the Information Given
1. From the problem, we know that the mother's age is twice that of the daughter's age:
\[ M = 2D \]

2. The father is 10 years older than the mother:
\[ F = M + 10 \]

3. The brother is 20 years younger than the mother:
\[ B = M - 20 \]

4. The brother is also 5 years older than the sister (daughter):
\[ B = D + 5 \]

### Step 3: Substitute and Solve
Now we can substitute the expression for \( M \) from the first equation into the other equations.

From \( B = M - 20 \):
\[ B = (2D) - 20 \]

From \( B = D + 5 \):
\[ D + 5 = (2D) - 20 \]

### Step 4: Rearranging the Equation
Now we will rearrange the equation to solve for \( D \):
\[ D + 5 = 2D - 20 \]
\[ 5 + 20 = 2D - D \]
\[ 25 = D \]

### Step 5: Find Mother's Age
Now that we have the daughter's age, we can find the mother's age:
\[ M = 2D = 2 \times 25 = 50 \]

### Step 6: Find Father's Age
Now we can find the father's age using the equation \( F = M + 10 \):
\[ F = 50 + 10 = 60 \]

### Conclusion
The age of the father is \( 60 \) years.

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