A student multiplied a number by `3/5` instead of `5/3` What is the by Instead of percentage error in the calcula tion ?

Options

A. 0.44
B. 0.34
C. 0.54
D. 0.64

Answer

To solve the problem of finding the percentage error in the student's calculation, we can follow these steps:

### Step 1: Define the number
Let the number be represented as \( N \). For simplicity, we can choose \( N = 15x \).

### Step 2: Calculate the incorrect result
The student multiplied the number by \( \frac{3}{5} \) instead of \( \frac{5}{3} \). Therefore, the incorrect calculation is:
\[ \text{Incorrect Result} = N \times \frac{3}{5} = 15x \times \frac{3}{5} \]
Calculating this gives:
\[ \text{Incorrect Result} = 15x \times \frac{3}{5} = 9x \]

### Step 3: Calculate the correct result
The correct calculation should have been:
\[ \text{Correct Result} = N \times \frac{5}{3} = 15x \times \frac{5}{3} \]
Calculating this gives:
\[ \text{Correct Result} = 15x \times \frac{5}{3} = 25x \]

### Step 4: Calculate the error
Now, we find the error in the calculation:
\[ \text{Error} = \text{Correct Result} - \text{Incorrect Result} = 25x - 9x = 16x \]

### Step 5: Calculate the percentage error
The percentage error is calculated using the formula:
\[ \text{Percentage Error} = \left( \frac{\text{Error}}{\text{Correct Result}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage Error} = \left( \frac{16x}{25x} \right) \times 100 \]
Simplifying this gives:
\[ \text{Percentage Error} = \left( \frac{16}{25} \right) \times 100 = 64\% \]

### Final Answer
The percentage error in the calculation is **64%**.

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