If a number is divided by 14, then it becomes equal to 10% of the second number. First number is how much percent more than the second number?

Options

A. `40%`
B. `45%`
C. `60%`
D. `30%`

Answer

To solve the problem step by step, let's define the variables and set up the equations based on the information provided.

### Step 1: Define the Variables
Let:
- First number = \( x \)
- Second number = \( y \)

### Step 2: Set Up the Equation
According to the problem, when the first number \( x \) is divided by 14, it becomes equal to 10% of the second number \( y \). This can be expressed mathematically as:
\[ \frac{x}{14} = 0.1y \]

### Step 3: Simplify the Equation
To eliminate the fraction, we can multiply both sides of the equation by 14:
\[ x = 14 \times 0.1y \]
This simplifies to:
\[ x = 1.4y \]

### Step 4: Convert to Fraction
We can express 1.4 as a fraction:
\[ x = \frac{14}{10}y = \frac{7}{5}y \]

### Step 5: Find the Difference
Now, we need to find how much more the first number \( x \) is compared to the second number \( y \):
\[ \text{Difference} = x - y = \frac{7}{5}y - y \]
To subtract, we convert \( y \) into a fraction with the same denominator:
\[ y = \frac{5}{5}y \]
Thus,
\[ \text{Difference} = \frac{7}{5}y - \frac{5}{5}y = \frac{2}{5}y \]

### Step 6: Calculate the Percentage Increase
To find out how much percent more \( x \) is than \( y \), we use the formula for percentage increase:
\[ \text{Percentage Increase} = \left(\frac{\text{Difference}}{y}\right) \times 100 \]
Substituting the difference we found:
\[ \text{Percentage Increase} = \left(\frac{\frac{2}{5}y}{y}\right) \times 100 = \left(\frac{2}{5}\right) \times 100 \]
This simplifies to:
\[ \text{Percentage Increase} = 40\% \]

### Conclusion
Thus, the first number is 40% more than the second number.