Q) 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.

Solution:The correct answer is \(\sqrt{5}\).
Explanation: Let the correct result be \( p \times q \). Instead, the student calculated \( \frac{p}{q} \). Let the percentage error be \( 80\% \). The percentage error can be expressed as: \[ \text{Percentage Error} = \frac{\left( \frac{p}{q} - p \times q \right)}{p \times q} \times 100 \] This simplifies to: \[ 80 = \frac{\left( \frac{p}{q} - p \times q \right)}{p \times q} \times 100 \] Let’s set up the ratio \( \frac{\frac{p}{q}}{p \times q} \), solve it, and use algebra to find that \( q = \sqrt{5} \).