GATE 2024 IN – Question 3
A student was supposed to multiply a positive real number $p$ by 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
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Correct answer: (D) $\sqrt5$
Explanation
The correct result is $pq$ and the student got $p/q$. The percentage error is $\dfrac{|p/q-pq|}{pq}\times100\%$.
$\dfrac{|p/q-pq|}{pq}=\left|\dfrac1{q^2}-1\right|=0.8$.
Either $1/q^2=0.2$, giving $q^2=5$, or $1/q^2=1.8$, giving $q=\sqrt5/3$, which is not among the options.
With $q>0$ the only option that satisfies the condition is $q=\sqrt5$, **D**.