If the ratio of two numbers is 2 : 1 and their product is 1800, then the greater number is—

Options

A. 90
B. 60
C. 30
D. 120

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the ratio
The ratio of the two numbers is given as 2:1. This means if we let the smaller number be \( x \), then the larger number can be represented as \( 2x \).

### Step 2: Set up the equation
According to the problem, the product of the two numbers is 1800. Therefore, we can write the equation:
\[ (2x) \cdot x = 1800 \]

### Step 3: Simplify the equation
This simplifies to:
\[ 2x^2 = 1800 \]

### Step 4: Solve for \( x^2 \)
To isolate \( x^2 \), divide both sides by 2:
\[ x^2 = \frac{1800}{2} = 900 \]

### Step 5: Solve for \( x \)
Now, take the square root of both sides to find \( x \):
\[ x = \sqrt{900} = 30 \]

### Step 6: Find the greater number
Since \( x \) represents the smaller number, the greater number (which is \( 2x \)) can be calculated as:
\[ 2x = 2 \cdot 30 = 60 \]

### Conclusion
Thus, the greater number is **60**.

---