A number whose double is 45 greater than its half is : Options are (a) 52 (b) 45 (c) 40 (d) 30.

Options

A. 52
B. 45
C. 40
D. 30

Answer

To solve the problem, we need to find a number \( x \) such that its double is 45 greater than its half. We can break this down step by step.

### Step 1: Define the variable
Let the number be \( x \).

### Step 2: Set up the equation
According to the problem, the double of the number \( x \) is equal to its half plus 45. We can express this mathematically as:
\[ 2x = \frac{x}{2} + 45 \]

### Step 3: Eliminate the fraction
To eliminate the fraction, we can multiply every term in the equation by 2 (the denominator):
\[ 2 \times 2x = 2 \times \left(\frac{x}{2} + 45\right) \]
This simplifies to:
\[ 4x = x + 90 \]

### Step 4: Rearrange the equation
Now, we will rearrange the equation to isolate \( x \). Subtract \( x \) from both sides:
\[ 4x - x = 90 \]
This simplifies to:
\[ 3x = 90 \]

### Step 5: Solve for \( x \)
Now, divide both sides by 3 to find \( x \):
\[ x = \frac{90}{3} = 30 \]

### Conclusion
The number we are looking for is \( x = 30 \).

### Final Answer
Thus, the correct option is (d) 30.

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