GATE 2024 BT – Question 59
A fermentor is filled with medium at a rate of 1 L min$^{-1}$. A leak develops at the bottom of the fermentor when the medium in the fermentor reaches 200 L. The rate of medium leakage is $2t$ L min$^{-1}$, where '$t$' is the time at which the leak begins.
The volume of medium in the fermentor after 10 min of leakage is ________ L (Answer in integer).
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Show answer and explanation
Correct answer: 110 to 110
Explanation
Taking $t$ as the time from the start of the leak, $\frac{dV}{dt} = 1 - 2t$, so $V = 200 + t - t^2 = 200 + 10 - 100 = 110$ L.
Official GATE 2024 answer key: https://gate2026.iitg.ac.in/doc/download/2024/BTFinalAnswerKey.pdf