If 40% of a number is 105 more than the one-fourth of that number, then what will be the difference between the number and 35% of the number?

Options

A. 315
B. 495
C. 455
D. 375

Answer

To solve the problem step by step, let's denote the unknown number as \( x \).

### Step 1: Set up the equation based on the problem statement
According to the problem, 40% of the number \( x \) is 105 more than one-fourth of that number. We can express this mathematically as:
\[ 0.4x = \frac{1}{4}x + 105 \]

### Step 2: Convert percentages to fractions
We know that 40% can be expressed as \( \frac{40}{100} = \frac{2}{5} \). Thus, we can rewrite the equation:
\[ \frac{2}{5}x = \frac{1}{4}x + 105 \]

### Step 3: Eliminate fractions by finding a common denominator
The least common multiple (LCM) of 5 and 4 is 20. We will multiply every term in the equation by 20 to eliminate the fractions:
\[ 20 \cdot \frac{2}{5}x = 20 \cdot \frac{1}{4}x + 20 \cdot 105 \]
This simplifies to:
\[ 8x = 5x + 2100 \]

### Step 4: Rearrange the equation to solve for \( x \)
Now, we will isolate \( x \) by subtracting \( 5x \) from both sides:
\[ 8x - 5x = 2100 \]
This simplifies to:
\[ 3x = 2100 \]

### Step 5: Solve for \( x \)
Now, divide both sides by 3 to find \( x \):
\[ x = \frac{2100}{3} = 700 \]

### Step 6: Find 35% of the number
Next, we need to calculate 35% of \( x \):
\[ 0.35x = 0.35 \times 700 = 245 \]

### Step 7: Calculate the difference between \( x \) and 35% of \( x \)
Finally, we find the difference between the number \( x \) and 35% of \( x \):
\[ x - 0.35x = 700 - 245 = 455 \]

### Final Answer
The difference between the number and 35% of the number is:
\[ \boxed{455} \]