The average age of a brother and sister was 35yr, 5yr ago. What will be their average age (in years) at present?

Options

A. `37.5`
B. 42
C. 40
D. `40.5`

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the given information
The average age of a brother and sister was 35 years, 5 years ago.

### Step 2: Set up the equation
Let the present age of the brother be \( x \) and the present age of the sister be \( y \).

Five years ago, their ages would have been \( x - 5 \) and \( y - 5 \). The average of their ages 5 years ago can be expressed as:
\[ \frac{(x - 5) + (y - 5)}{2} = 35 \]

### Step 3: Simplify the equation
Now, simplify the equation:
\[ \frac{x + y - 10}{2} = 35 \]
Multiplying both sides by 2 to eliminate the fraction:
\[ x + y - 10 = 70 \]
Adding 10 to both sides gives:
\[ x + y = 80 \]

### Step 4: Calculate the present average age
To find the present average age of the brother and sister, we can use the equation:
\[ \text{Average present age} = \frac{x + y}{2} \]
Substituting \( x + y = 80 \):
\[ \text{Average present age} = \frac{80}{2} = 40 \]

### Final Answer
The average age of the brother and sister at present is **40 years**.

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