Question

A student was supposed to multiply a positive real number \( p \) with another positive real number \( q \). Instead, the student divided \( p \) by \( q \). If the percentage error in the student’s answer is 80\%, the value of \( q \) is:

• A. \( \sqrt{2} \)
• B. \( 2 \)
• C. \( 4 \)
• D. \( 5 \)

Hint:

When solving error-based problems, carefully set up the equation by comparing the expected and actual operations.

Answer 1

The Correct Option is D

Step 1: Setting up the error equation. The percentage error is given by: \[ {Error} = \left| \frac{\frac{p}{q} - pq}{pq} \right| \times 100 = 80\%. \] Step 2: Solving for \( q \). Simplifying the equation: \[ \frac{1}{q^2} - 1 = -0.8 \quad \Rightarrow \quad q^2 = 5 \quad \Rightarrow \quad q = \sqrt{5}. \] Step 3: Conclusion. The value of \( q \) is \( \sqrt{5} \), which corresponds to option \( {(4)} \).