If one-nineth of a certain number exceeds its one-tenth by 4, the number is

Options

A. 320
B. 360
C. 400
D. 440

Answer

To solve the problem, we need to find the number \( x \) such that one-ninth of \( x \) exceeds one-tenth of \( x \) by 4.

### Step-by-Step Solution:

1. **Set Up the Equation**:
We start by expressing the information given in the problem mathematically.
\[ \frac{x}{9} = \frac{x}{10} + 4 \]

2. **Eliminate the Fractions**:
To eliminate the fractions, we can find a common multiple of the denominators (9 and 10). The least common multiple (LCM) of 9 and 10 is 90. We will multiply the entire equation by 90:
\[ 90 \cdot \frac{x}{9} = 90 \cdot \left(\frac{x}{10} + 4\right) \]
This simplifies to:
\[ 10x = 9x + 360 \]

3. **Rearrange the Equation**:
Next, we will rearrange the equation to isolate \( x \):
\[ 10x - 9x = 360 \]
Simplifying this gives:
\[ x = 360 \]

4. **Conclusion**:
Therefore, the number is \( x = 360 \).

### Final Answer:
The number is **360**.

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