The personnel costs of a company are 41 % of their total costs. Company needs to cut down their total costs by 18%. However, the personnel costs have decreased only by 5%. How many percent do they need to be able to cut down other costs to achieve the goal?
Give all answers with all decimals.

We are given the following information:

- Personnel costs represent 41% of the total costs.
- The company aims to reduce its total costs by 18%.
- Personnel costs have only decreased by 5%.

Let:
- \( C_{\text{total}} \) represent the total costs of the company.
- \( C_{\text{personnel}} = 0.41 \times C_{\text{total}} \) represent the personnel costs.
- \( C_{\text{other}} = 0.59 \times C_{\text{total}} \) represent the other costs.

### Step 1: Reduction in Personnel Costs
The personnel costs decrease by 5%, so the new personnel costs are:
\[
C_{\text{new personnel}} = (1 - 0.05) \times C_{\text{personnel}} = 0.95 \times 0.41 \times C_{\text{total}} = 0.3895 \times C_{\text{total}}
\]

### Step 2: Total Costs Reduction Target
The total cost needs to decrease by 18%, so the new total costs should be:
\[
C_{\text{new total}} = (1 - 0.18) \times C_{\text{total}} = 0.82 \times C_{\text{total}}
\]

### Step 3: Remaining Reduction Needed from Other Costs
The new total costs are made up of the new personnel costs and the new other costs. Let \( C_{\text{new other}} \) represent the new other costs. We can write:
\[
C_{\text{new total}} = C_{\text{new personnel}} + C_{\text{new other}}
\]
Substituting the expressions for \( C_{\text{new total}} \) and \( C_{\text{new personnel}} \):
\[
0.82 \times C_{\text{total}} = 0.3895 \times C_{\text{total}} + C_{\text{new other}}
\]
Solve for \( C_{\text{new other}} \):
\[
C_{\text{new other}} = 0.82 \times C_{\text{total}} - 0.3895 \times C_{\text{total}} = 0.4305 \times C_{\text{total}}
\]

### Step 4: Required Reduction in Other Costs
The original other costs are \( 0.59 \times C_{\text{total}} \). The reduction in other costs is the percentage change from the original to the new other costs:
\[
\text{Reduction in other costs} = \frac{0.59 - 0.4305}{0.59} = \frac{0.1595}{0.59}
\]
Calculating this:
\[
\text{Reduction in other costs} = 0.27033898305
\]

Therefore, the other costs need to be reduced by approximately **27.0339%**.

Would you like more details or have any questions?

Here are 5 related questions to expand on this topic:
1. How does a change in fixed costs impact overall cost reduction strategies?
2. If the personnel costs were initially higher, how would that affect the required reduction in other costs?
3. What if the company could only reduce the other costs by 20%? How would that impact the total cost reduction?
4. How would a 10% increase in non-personnel-related costs affect the company's overall cost-cutting goal?
5. How can companies optimize personnel costs without reducing headcount?

**Tip:** When calculating percentage reductions, always focus on the relative proportion of each component to the whole.

The personnel costs of a company are 41% of their total costs. Company needs to cut down their total costs by 18%. However, the personnel costs have decreased only by 5%. How many percent do they need to be able to cut down other costs to achieve the goal?

Learn how to calculate the necessary reduction in other costs to achieve a company's goal of reducing total costs by 18%, when personnel costs decrease by only 5%. Understand key concepts like percentage decrease and cost allocation in this step-by-step solution.

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