Among four friends, Govind is twice the age of Krishan. Nandu is half of the age of Krishan. Gwala is 6 years elder to Krishan, but . 6 years younger then Govind. Who is the youngest ?

Options

A. Govind
B. Krishan
C. Nandu
D. Cannot be determined

Explanation

To solve the problem step by step, we will define the ages of each friend based on the information given.

### Step 1: Define the variables
Let the age of Krishan be represented as \( K \).

### Step 2: Express the ages of the other friends in terms of \( K \)
- **Govind's age**: According to the problem, Govind is twice the age of Krishan. Therefore, we can express Govind's age as:
\[ G = 2K \]
- **Nandu's age**: Nandu is half the age of Krishan. Thus, we can express Nandu's age as:
\[ N = \frac{K}{2} \]
- **Gwala's age**: Gwala is 6 years older than Krishan. Hence, we can express Gwala's age as:
\[ Gw = K + 6 \]
Additionally, Gwala is also 6 years younger than Govind, which gives us another equation:
\[ Gw = G - 6 \]
Substituting \( G \) from our earlier expression:
\[ Gw = 2K - 6 \]

### Step 3: Set up the equation
Now we have two expressions for Gwala's age:
1. \( Gw = K + 6 \)
2. \( Gw = 2K - 6 \)

We can set these two equations equal to each other:
\[ K + 6 = 2K - 6 \]

### Step 4: Solve for \( K \)
Rearranging the equation:
\[ 6 + 6 = 2K - K \]
\[ 12 = K \]

### Step 5: Calculate the ages of all friends
Now that we have \( K \), we can find the ages of all friends:
- **Krishan's age**:
\[ K = 12 \]
- **Govind's age**:
\[ G = 2K = 2 \times 12 = 24 \]
- **Nandu's age**:
\[ N = \frac{K}{2} = \frac{12}{2} = 6 \]
- **Gwala's age**:
\[ Gw = K + 6 = 12 + 6 = 18 \]

### Step 6: Determine the youngest
Now we compare the ages:
- Govind: 24 years
- Krishan: 12 years
- Gwala: 18 years
- Nandu: 6 years

From the ages calculated, it is clear that Nandu is the youngest.

### Final Answer
**Nandu is the youngest.**