If (x + 25% of 270 is 20% more than x% of 240, then 12% of (x + 125) is what per cent more than 10% of x?

Options

A. 55
B. 45
C. 42
D. 60

Answer

To solve the problem step by step, let's break it down into manageable parts.

### Step 1: Understand the given equation
We are given that:
\[ x + 25\% \text{ of } 270 = 20\% \text{ more than } x\% \text{ of } 240 \]

### Step 2: Calculate 25% of 270
Calculate \( 25\% \text{ of } 270 \):
\[ 25\% \text{ of } 270 = \frac{25}{100} \times 270 = 67.5 \]

### Step 3: Set up the equation
Now, substitute this value into the equation:
\[ x + 67.5 = 1.2 \times (x\% \text{ of } 240) \]

### Step 4: Calculate x% of 240
Calculate \( x\% \text{ of } 240 \):
\[ x\% \text{ of } 240 = \frac{x}{100} \times 240 = 2.4x \]

### Step 5: Substitute back into the equation
Now, substitute \( 2.4x \) into the equation:
\[ x + 67.5 = 1.2 \times 2.4x \]

### Step 6: Simplify the equation
Calculate \( 1.2 \times 2.4 \):
\[ 1.2 \times 2.4 = 2.88 \]
So the equation becomes:
\[ x + 67.5 = 2.88x \]

### Step 7: Rearrange the equation
Rearranging gives:
\[ 67.5 = 2.88x - x \]
\[ 67.5 = 1.88x \]

### Step 8: Solve for x
Now, solve for \( x \):
\[ x = \frac{67.5}{1.88} \approx 35.85 \]

### Step 9: Calculate \( x + 125 \)
Now calculate \( x + 125 \):
\[ x + 125 = 35.85 + 125 = 160.85 \]

### Step 10: Calculate 12% of \( x + 125 \)
Calculate \( 12\% \text{ of } 160.85 \):
\[ 12\% \text{ of } 160.85 = \frac{12}{100} \times 160.85 = 19.302 \]

### Step 11: Calculate 10% of x
Calculate \( 10\% \text{ of } x \):
\[ 10\% \text{ of } 35.85 = \frac{10}{100} \times 35.85 = 3.585 \]

### Step 12: Find the difference
Now find how much more \( 19.302 \) is than \( 3.585 \):
\[ 19.302 - 3.585 = 15.717 \]

### Step 13: Calculate the percentage increase
To find what percent more \( 19.302 \) is than \( 3.585 \):
\[ \text{Percentage increase} = \left( \frac{15.717}{3.585} \right) \times 100 \approx 438.3\% \]

Thus, the final answer is approximately \( 438.3\% \).