The age of Ram is double that of Shyam and half the of Sohan. Shyam is older than Mohan. Who is the oldest ?

Options

A. (a) Mohan
B. (b) Ram
C. (c) Sohan
D. (d) Shyam

Explanation

To solve the problem step by step, we can define the ages of Ram, Shyam, Sohan, and Mohan using algebraic expressions.

### Step 1: Define the ages
Let the age of Shyam be \( S \). According to the problem:
- The age of Ram \( R \) is double that of Shyam:
\[ R = 2S \]
- The age of Sohan \( H \) is double that of Ram:
\[ H = 2R \]
Substituting the expression for \( R \) into the equation for \( H \):
\[ H = 2(2S) = 4S \]

### Step 2: Compare the ages
Now we have the ages expressed in terms of Shyam's age:
- Ram's age \( R = 2S \)
- Sohan's age \( H = 4S \)
- Shyam's age \( S = S \)

### Step 3: Consider Mohan's age
The problem states that Shyam is older than Mohan. Therefore, we can denote Mohan's age as \( M \) such that:
\[ M < S \]

### Step 4: Determine the oldest
Now we compare the ages:
- Sohan's age \( H = 4S \)
- Ram's age \( R = 2S \)
- Shyam's age \( S \)
- Mohan's age \( M < S \)

From these comparisons, we can see that:
- Sohan is the oldest because \( H = 4S \) is greater than both \( R \) and \( S \), and Mohan is younger than Shyam.

### Conclusion
Thus, the oldest person among Ram, Shyam, Sohan, and Mohan is **Sohan**.

### Final Answer
Sohan is the oldest.

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