A father gives money to three of his sons, Ramu, Shamu and Dhamu, in the ratio 7:5:9 respectively. If Dhamu gets 120 more than Shamu, how much does Ramu get?

Options

A. A) 150
B. B) 300
C. C) 420
D. D) 210

Answer

To solve the problem step by step, we will follow the given information and use algebra to find out how much Ramu gets.

### Step 1: Understand the Ratio
The father gives money to his three sons, Ramu, Shamu, and Dhamu, in the ratio of 7:5:9. This means:
- Ramu gets 7 parts,
- Shamu gets 5 parts,
- Dhamu gets 9 parts.

### Step 2: Assign Variables
Let’s assume that each part is represented by a variable \( x \).
- Ramu's amount = \( 7x \)
- Shamu's amount = \( 5x \)
- Dhamu's amount = \( 9x \)

### Step 3: Set Up the Equation
According to the problem, Dhamu gets 120 more than Shamu. We can express this relationship as:
\[ 9x = 5x + 120 \]

### Step 4: Solve the Equation
Now, we will solve the equation for \( x \):
1. Subtract \( 5x \) from both sides:
\[ 9x - 5x = 120 \]
This simplifies to:
\[ 4x = 120 \]
2. Divide both sides by 4:
\[ x = \frac{120}{4} = 30 \]

### Step 5: Calculate Ramu's Amount
Now that we have the value of \( x \), we can find out how much Ramu gets:
\[ \text{Ramu's amount} = 7x = 7 \times 30 = 210 \]

### Conclusion
Thus, Ramu gets **210 rupees**.

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