A student was asked to simplify `(0.6xx0.6xx0.6+0.5xx0.5xx0.5+0.1xx0.1xx0.1-0.09)/(0.6xx0.6+0.5xx0.5+0.1xx0.1-0.41)` and his answer was 0.6 By what per cent was his answer wrong.

Options

A. `25%`
B. `100%`
C. `50%`
D. `120%`

Answer

To solve the problem step by step, we will simplify the expression given in the question and then calculate the percentage error in the student's answer.

### Step 1: Simplify the numerator
The numerator of the expression is:
\[ 0.6 \times 0.6 \times 0.6 + 0.5 \times 0.5 \times 0.5 + 0.1 \times 0.1 \times 0.1 - 0.09 \]
Calculating each term:
- \(0.6 \times 0.6 \times 0.6 = 0.6^3 = 0.216\)
- \(0.5 \times 0.5 \times 0.5 = 0.5^3 = 0.125\)
- \(0.1 \times 0.1 \times 0.1 = 0.1^3 = 0.001\)

Now substituting these values into the numerator:
\[ 0.216 + 0.125 + 0.001 - 0.09 \]
Calculating this step by step:
\[ 0.216 + 0.125 = 0.341 \]
\[ 0.341 + 0.001 = 0.342 \]
\[ 0.342 - 0.09 = 0.252 \]

So, the numerator simplifies to:
\[ 0.252 \]

### Step 2: Simplify the denominator
The denominator of the expression is:
\[ 0.6 \times 0.6 + 0.5 \times 0.5 + 0.1 \times 0.1 - 0.41 \]
Calculating each term:
- \(0.6 \times 0.6 = 0.36\)
- \(0.5 \times 0.5 = 0.25\)
- \(0.1 \times 0.1 = 0.01\)

Now substituting these values into the denominator:
\[ 0.36 + 0.25 + 0.01 - 0.41 \]
Calculating this step by step:
\[ 0.36 + 0.25 = 0.61 \]
\[ 0.61 + 0.01 = 0.62 \]
\[ 0.62 - 0.41 = 0.21 \]

So, the denominator simplifies to:
\[ 0.21 \]

### Step 3: Calculate the overall expression
Now we can calculate the overall expression:
\[ \frac{0.252}{0.21} \]
Calculating this:
\[ \frac{0.252}{0.21} = 1.2 \]

### Step 4: Calculate the percentage error
The student's answer was \(0.6\) and our calculated answer is \(1.2\). To find the percentage error:
1. Find the difference between the correct answer and the student's answer:
\[ 1.2 - 0.6 = 0.6 \]
2. Calculate the percentage error:
\[ \text{Percentage Error} = \left(\frac{\text{Difference}}{\text{Correct Answer}}\right) \times 100 = \left(\frac{0.6}{1.2}\right) \times 100 = 50\% \]

### Final Answer
The student's answer was wrong by **50%**.

---