If `37 1/2%` of a number is 900.Find the number

Options

A. 1200
B. 1350
C. 2400
D. 540

Answer

To solve the problem, we need to find the number \( X \) such that \( 37 \frac{1}{2} \% \) of \( X \) equals 900. Let's break this down step by step.

### Step 1: Convert the percentage to a fraction
First, we convert \( 37 \frac{1}{2} \% \) into a fraction.

\[ 37 \frac{1}{2} = 37.5 = \frac{75}{2} \]

So,

\[ 37 \frac{1}{2} \% = \frac{75}{2} \div 100 = \frac{75}{200} = \frac{3}{8} \]

### Step 2: Set up the equation
Now, we can set up the equation based on the information given in the problem:

\[ \frac{3}{8} \times X = 900 \]

### Step 3: Solve for \( X \)
To find \( X \), we need to isolate it. We can do this by multiplying both sides of the equation by the reciprocal of \( \frac{3}{8} \), which is \( \frac{8}{3} \):

\[ X = 900 \times \frac{8}{3} \]

### Step 4: Calculate \( X \)
Now we perform the multiplication:

\[ X = 900 \times \frac{8}{3} = 900 \div 3 \times 8 = 300 \times 8 = 2400 \]

Thus, the value of \( X \) is:

\[ X = 2400 \]

### Final Answer
The number is \( 2400 \).

---