# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-5/8

Exercises: Try Out - Set 5: Real exam simulation to sharpen your skills and build confidence. - Problem 8

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## Exercise 8

### Question

export const metadata = {
  title: "Problem 8",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/23/2025",
};

To complete the construction of a bridge, <InlineMath math="24" /> workers are needed and it is targeted to be finished in <InlineMath math="35" /> days. After <InlineMath math="8" /> days of work, half of the workers stop working. To ensure the bridge construction is completed, additional time of ... days is needed.


### Choices

- [ ] $$54$$
- [ ] $$38$$
- [ ] $$28$$
- [ ] $$14$$
- [x] $$19$$

### Answer & Explanation

export const metadata = {
  title: "Solution to Problem 8",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/23/2025",
};

We can solve this problem using the concept of inverse proportion or total workload (man-days).

#### Calculating Workload

The total planned workload is:
<MathContainer>
  <BlockMath math="\text{Total Workload} = 24 \text{ workers} \times 35 \text{ days}" />
</MathContainer>

The work is divided into two phases:
1. First phase: <InlineMath math="24" /> workers work for <InlineMath math="8" /> days.
2. Second phase: Half of the workers stop, so <InlineMath math="24 / 2 = 12" /> workers remain working for <InlineMath math="P" /> days.

The equation is:

<MathContainer>
  <BlockMath math="24 \times 35 = (24 \times 8) + (12 \times P)" />
</MathContainer>

#### Finding the Value of P

We solve the equation above to find <InlineMath math="P" /> (the duration for the remaining project).

<MathContainer>
  <BlockMath math="840 = 192 + 12P" />
  <BlockMath math="840 - 192 = 12P" />
  <BlockMath math="648 = 12P" />
  <BlockMath math="P = \frac{648}{12}" />
  <BlockMath math="P = 54" />
</MathContainer>

So, the time needed to complete the remaining work with <InlineMath math="12" /> workers is <InlineMath math="54" /> days.

#### Calculating Additional Time

Based on the provided solution, the additional time is calculated as the difference between the duration of the remaining work (<InlineMath math="P" />) and the total initial target (<InlineMath math="35" /> days).

<MathContainer>
  <BlockMath math="\text{Additional days} = 54 - 35 = 19 \text{ days}" />
</MathContainer>

Thus, <InlineMath math="19" /> additional days are needed.


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