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
The correct answer is $pq$ and the student got $\frac{p}{q}$. The relative error is $\left|\frac{p/q - pq}{pq}\right| = \left|\frac{1}{q^2} - 1\right| = 0.8$. So $\frac{1}{q^2} = 0.2$ or $1.8$, that is $q^2 = 5$ or $q^2 = 0.556$. Only $q = \sqrt{5}$ is among the options.
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