Rahul is 4 years younger than his elder brother Shyam. Rahul also has a sister who is 3 years younger to him. What is the difference between the age of Rahul and the average age of the three siblings?

Options

A. a. 6 months
B. b. 4 months
C. c. 2 months
D. d. 8 months

Answer

To solve the problem step by step, we will define the ages of the siblings and then calculate the required difference.

### Step 1: Define Rahul's Age
Let Rahul's age be \( x \).

### Step 2: Define Shyam's Age
Since Rahul is 4 years younger than his elder brother Shyam, we can express Shyam's age as:
\[ \text{Shyam's age} = x + 4 \]

### Step 3: Define Sister's Age
Rahul has a sister who is 3 years younger than him. Therefore, we can express his sister's age as:
\[ \text{Sister's age} = x - 3 \]

### Step 4: Calculate the Average Age of the Siblings
To find the average age of the three siblings, we add their ages together and divide by 3:
\[ \text{Average age} = \frac{\text{Rahul's age} + \text{Shyam's age} + \text{Sister's age}}{3} \]
Substituting the ages we defined:
\[ \text{Average age} = \frac{x + (x + 4) + (x - 3)}{3} \]
Simplifying the expression:
\[ = \frac{x + x + 4 + x - 3}{3} = \frac{3x + 1}{3} \]

### Step 5: Find the Difference Between Rahul's Age and the Average Age
Now we need to find the difference between Rahul's age and the average age:
\[ \text{Difference} = \text{Average age} - \text{Rahul's age} \]
Substituting the values:
\[ \text{Difference} = \frac{3x + 1}{3} - x \]
To combine the terms, we express \( x \) as a fraction:
\[ = \frac{3x + 1}{3} - \frac{3x}{3} = \frac{3x + 1 - 3x}{3} = \frac{1}{3} \]

### Step 6: Convert the Difference to Months
The difference we found is \( \frac{1}{3} \) years. To convert this into months:
\[ \frac{1}{3} \text{ years} = \frac{12 \text{ months}}{3} = 4 \text{ months} \]

### Final Answer
The difference between Rahul's age and the average age of the three siblings is **4 months**.

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