Question

A person multiplied a number by\(\frac{7}{13}\)instead of\(\frac{17}{13}\).What is the percentage of error in the calculation?

• A. 58.62
• B. 58.82
• C. 58.02
• D. 58.42

Answer 1

The Correct Option is B

Finding the Percentage Error: 

Step 1: Define the Original Number

Let the original number be \( X \).

Step 2: Correct and Incorrect Multiplication

• Correct multiplication: \[ X \times \frac{17}{13} \]
• Incorrect multiplication: \[ X \times \frac{7}{13} \]

Step 3: Error in Calculation

The difference (error) between correct and incorrect values:

\[ X \times \frac{17}{13} - X \times \frac{7}{13} = X \times \frac{10}{13} \]

Step 4: Percentage Error

The formula for percentage error is:

\[ \frac{\text{Error}}{\text{Correct value}} \times 100 \]

Substituting the values: \[ \frac{\frac{10}{13}X}{\frac{17}{13}X} \times 100 \]

\[ \frac{10}{17} \times 100 = 58.82\% \]

Final Answer:

Thus, the correct answer is 58.82% (Option B).