The age of Ram is double as that of Shyam and half as that of Suresh. If the sum of their ages is 70, what is the age of Ram ?

Options

A. 20
B. 30
C. 40
D. 10

Explanation

To solve the problem step by step, we can define the ages of Ram, Shyam, and Suresh using variables based on the relationships given in the question.

### Step-by-Step Solution:

1. **Define Variables:**
- Let the age of Shyam be \( x \).
- According to the problem, Ram's age is double that of Shyam, so Ram's age will be \( 2x \).
- Also, Ram's age is half that of Suresh, which means Suresh's age will be \( 2 \times (2x) = 4x \).

2. **Set Up the Equation:**
- The sum of their ages is given as 70. Therefore, we can write the equation:
\[ x + 2x + 4x = 70 \]

3. **Combine Like Terms:**
- Combine the terms on the left side:
\[ 7x = 70 \]

4. **Solve for \( x \):**
- To find \( x \), divide both sides of the equation by 7:
\[ x = \frac{70}{7} = 10 \]

5. **Find Ram's Age:**
- Now that we have \( x \), we can find Ram's age:
\[ \text{Ram's age} = 2x = 2 \times 10 = 20 \]

### Conclusion:
The age of Ram is **20 years**.

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