# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-7/15

Exercises: Try Out - Set 7: Real exam simulation to sharpen your skills and build confidence. - Problem 15

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## Exercise 15

### Question

export const metadata = {
  title: "Problem 15",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/26/2025",
};

Joko's water tank can hold <InlineMath math="86" /> liters of water. Unfortunately, the tank is cracked, causing a leak of between <InlineMath math="0.3" /> liters and <InlineMath math="0.7" /> liters per hour. At <InlineMath math="07.00" /> AM, Joko filled his tank completely. Between <InlineMath math="07.00 - 11.00" />, there was no refilling or water usage. Which of the following relationships between quantities <InlineMath math="P" /> and <InlineMath math="Q" /> is correct based on the given information?

| <InlineMath math="P" /> | <InlineMath math="Q" /> |
| :---: | :--- |
| <InlineMath math="83.1" /> liters | Volume of water at <InlineMath math="11.00" /> |


### Choices

- [ ] $$P > Q$$
- [x] $$P < Q$$
- [ ] $$P = Q$$
- [ ] $$P + Q = 80$$
- [ ] Cannot be determined

### Answer & Explanation

export const metadata = {
  title: "Explanation for Problem 15",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/26/2025",
};

Given:
- Initial water volume = <InlineMath math="86" /> liters.
- Leakage per hour (<InlineMath math="x" />) is between <InlineMath math="0.3" /> and <InlineMath math="0.7" /> liters. This means <InlineMath math="0.3 < x < 0.7" />.
- The observation time is from <InlineMath math="07.00" /> to <InlineMath math="11.00" />, which is <InlineMath math="4" /> hours.

We calculate the range of water leaked over <InlineMath math="4" /> hours:

<MathContainer>
  <BlockMath math="4(0.3) < 4x < 4(0.7)" />
  <BlockMath math="1.2 < 4x < 2.8" />
</MathContainer>

So, the total water leaked is between <InlineMath math="1.2" /> liters and <InlineMath math="2.8" /> liters.

Next, we calculate the remaining water volume (<InlineMath math="Q" />) at <InlineMath math="11.00" />. The volume <InlineMath math="Q" /> is the initial volume minus the total leakage:

<MathContainer>
  <BlockMath math="Q = 86 - 4x" />
</MathContainer>

Since the total leakage is between <InlineMath math="1.2" /> and <InlineMath math="2.8" /> liters, the range for <InlineMath math="Q" /> is:
- Lower bound of <InlineMath math="Q" /> (maximum leakage): <InlineMath math="86 - 2.8 = 83.2" /> liters.
- Upper bound of <InlineMath math="Q" /> (minimum leakage): <InlineMath math="86 - 1.2 = 84.8" /> liters.

Thus, <InlineMath math="83.2 < Q < 84.8" />.

Now we compare <InlineMath math="P" /> and <InlineMath math="Q" />:
- <InlineMath math="P = 83.1" /> liters.
- The minimum value of <InlineMath math="Q" /> is greater than <InlineMath math="83.2" /> liters.

Since <InlineMath math="83.1 < 83.2" />, the value of <InlineMath math="P" /> is always smaller than the minimum possible value of <InlineMath math="Q" />.

Therefore, <InlineMath math="P < Q" />.


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