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URL: https://nakafa.com/en/exercises/high-school/snbt/mathematical-reasoning/try-out/2026/set-1/15

Exercises: Try Out 2026 - Set 1: Real exam simulation to sharpen your skills and build confidence. - Question 15

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## Exercise 15

### Question

export const metadata = {
  title: "Question 15",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "11/23/2025",
};

A building construction project is completed in <InlineMath math="50 \text{ working days }" /> with the help of <InlineMath math="80 \text{ workers }" />.

If the project is to be completed in <InlineMath math="40 \text{ days }" /> assuming each worker has the same ability, the number of additional workers needed so that the project can be completed as planned is ... people.



### Choices

- [x] $$20$$
- [ ] $$40$$
- [ ] $$60$$
- [ ] $$80$$
- [ ] $$100$$

### Answer & Explanation

export const metadata = {
  title: "Solution for Question 15",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "11/23/2025",
};

We will use the concept of inverse proportion to determine the total number of workers needed, then calculate the difference with the initial number of workers.

#### Calculating Total Workload

The total project workload is constant, which is:

<MathContainer>
  <BlockMath math="\text{Total Workload} = \text{Initial Workers} \times \text{Initial Time}" />
  <BlockMath math="\text{Total Workload} = 80 \times 50 = 4{,}000 \text{ man-days}" />
</MathContainer>

#### Calculating Required Number of Workers

If the completion time is accelerated to <InlineMath math="40 \text{ days }" />, the number of workers required (<InlineMath math="P" />) is:

<MathContainer>
  <BlockMath math="P \times 40 = 4{,}000" />
  <BlockMath math="P = \frac{4{,}000}{40}" />
  <BlockMath math="P = 100 \text{ people}" />
</MathContainer>

#### Calculating Additional Workers

The existing number of workers is <InlineMath math="80" />. Thus, the additional workers needed are:

<MathContainer>
  <BlockMath math="\text{Additional} = \text{Required Workers} - \text{Initial Workers}" />
  <BlockMath math="\text{Additional} = 100 - 80 = 20 \text{ people}" />
</MathContainer>

So, the number of additional workers needed is **<InlineMath math="20 \text{ people}" />**.



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