If two times of the daughter’s age in years is included to the mother’s age, the total is 70 and if two times of the mother’s age is included to the daughter’s age, the total is 95. So the Mother’s age is,

Options

A. A. 38
B. B. 41
C. C. 42
D. D. 40

Answer

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

### Step 1: Define the Variables
Let:
- A = Daughter's age
- B = Mother's age

### Step 2: Set Up the Equations
From the problem statement, we can derive the following equations:

1. According to the first statement: "If two times the daughter’s age is included to the mother’s age, the total is 70."
\[ 2A + B = 70 \quad \text{(Equation 1)} \]

2. According to the second statement: "If two times the mother’s age is included to the daughter’s age, the total is 95."
\[ A + 2B = 95 \quad \text{(Equation 2)} \]

### Step 3: Solve the Equations
We can solve these two equations simultaneously. Let's manipulate Equation 2 first.

**Multiply Equation 2 by 2:**
\[ 2(A + 2B) = 2 \times 95 \]
This simplifies to:
\[ 2A + 4B = 190 \quad \text{(Equation 3)} \]

### Step 4: Subtract Equation 1 from Equation 3
Now we will subtract Equation 1 from Equation 3:
\[ (2A + 4B) - (2A + B) = 190 - 70 \]
This simplifies to:
\[ 4B - B = 120 \]
\[ 3B = 120 \]

### Step 5: Solve for B
Now, divide both sides by 3:
\[ B = \frac{120}{3} = 40 \]

### Step 6: Conclusion
Thus, the mother's age (B) is 40 years.